# Logical Reasoning - Logical Deduction - Discussion

Discussion Forum : Logical Deduction - Section 1 (Q.No. 2)

*Directions to Solve*

In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Give answer:

- (A) If only conclusion I follows
- (B) If only conclusion II follows
- (C) If either I or II follows
- (D) If neither I nor II follows and
- (E) If both I and II follow.

2.

**Statements: **All bags are cakes. All lamps are cakes.

**Conclusions:**

- Some lamps are bags.
- No lamp is bag.

Answer: Option

Explanation:

Since the middle term 'cakes' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.

Discussion:

57 comments Page 1 of 6.
Isaac Neebo said:
1 year ago

I think D is the right answer:

All Bags(B)=Cakes(C)

All Lamps (L)=Cakes(C)

Therefore all B = L

This is a form of Hypothetical syllogism.

So any answer different from this does not follow logically.

All Bags(B)=Cakes(C)

All Lamps (L)=Cakes(C)

Therefore all B = L

This is a form of Hypothetical syllogism.

So any answer different from this does not follow logically.

(1)

Jvd said:
1 year ago

Why is it not option B?

The second statement can be rewritten as "All lamps are not cakes". "not cakes" would refer to anything that isn't cake, including bags. This would give us one of the many possible variations of the statement: "All lamps are not bags".

The second statement can be rewritten as "All lamps are not cakes". "not cakes" would refer to anything that isn't cake, including bags. This would give us one of the many possible variations of the statement: "All lamps are not bags".

(2)

Reddy said:
2 years ago

The correct answer is A.

(3)

Andrew said:
2 years ago

Rule 8

If both premises are Affirmative, the conclusion must be Affirmative.

Rule 9

If both premises are Universal, the conclusion must be Universal.

All bags are cakes is Universal Affirmative

All lamps are cakes is Universal Affirmative.

So rules 8 & 9 apply

Some lamps are bags is Particular Affirmative.

No lamp is bag is Universal Negative.

These two conclusions cannot follow because they violate rules 8 & 9.

As for the middle term (a term common to both premises)

Cakes is the middle term since it is common to both premises.

Conclusions

Some lamps are bags

No lamp is a bag.

In both conclusions, the bag is the predicate while ( bag is the major term)

The lamp is the subject of both conclusions ( lamp is the minor term)

The major premise is that proposition/ premise in which the middle term is the subject.

The minor premise is that in which the middle term is the predicate.

In both premises cakes (the middle term is the predicate) meaning that none of the premises is a "Major Premise".

Both premises are " Minor premises".

All bags are cakes - Bags are distributed since bags is subject here.

All lamps are cakes - Lamps are distributed here as well.

Rule 1.

The conclusion doesn't contain the middle term. If both conclusions contain the middle term ( cakes) neither of them can follow.

Rule 2.

No 'term' can be distributed in the conclusion unless it's distributed in the premises.

Conclusion ' No lamps is bags' has lamps being distributed just like the premise " All lamps are cakes" has lamps being distributed.

Therefore Rule 2 is observed ( meaning we should have a viable conclusion to follow).

Rule 3

The middle term should be distributed at least once in the premises.

Cakes the middle term is not distributed in any of the premises.

And as such, the conclusion cannot follow.

Rule 4, of circumstances under which no conclusion follows, is not applicable because;

a) both premises are particular ( both premises are Universal - All).

b) both premises are negative ( both are Affirmative).

c) major premise is particular and the minor is negative ( both premises are Minor & Positive/Affirmative).

This would suggest we expect to have a conclusion to follow.

Rule 5

If the middle term is distributed twice, the conclusion is universal.

The middle term cakes is not distributed at all.

So, this rule is not applicable.

Rule 6.

The conclusion must be negative if one premise is negative.

Both premises are positive/affirmative.

So this rule is not applicable.

Rule 7,

The conclusion must be Particular if one premise is particular.

Both premises are Universal.

So this rule is not applicable.

In Mathematics, BODMAS is a Standard Rules Guide on which 'rule/procedure' is executed before the other.

If this logical deduction is not subjective (is STANDARD), what is the standard guiding protocol for resolving these logical deductions?

Is it the immediate deductive inference that is considered before the mediate deductive inference or vice versa?

Or is it the Venn diagrams deduction approach that is prime with the other two followings?

Or is it this subjective adoption of the rules as per the person setting these questions?

Anyone please clarify this.

If both premises are Affirmative, the conclusion must be Affirmative.

Rule 9

If both premises are Universal, the conclusion must be Universal.

All bags are cakes is Universal Affirmative

All lamps are cakes is Universal Affirmative.

So rules 8 & 9 apply

Some lamps are bags is Particular Affirmative.

No lamp is bag is Universal Negative.

These two conclusions cannot follow because they violate rules 8 & 9.

As for the middle term (a term common to both premises)

Cakes is the middle term since it is common to both premises.

Conclusions

Some lamps are bags

No lamp is a bag.

In both conclusions, the bag is the predicate while ( bag is the major term)

The lamp is the subject of both conclusions ( lamp is the minor term)

The major premise is that proposition/ premise in which the middle term is the subject.

The minor premise is that in which the middle term is the predicate.

In both premises cakes (the middle term is the predicate) meaning that none of the premises is a "Major Premise".

Both premises are " Minor premises".

All bags are cakes - Bags are distributed since bags is subject here.

All lamps are cakes - Lamps are distributed here as well.

Rule 1.

The conclusion doesn't contain the middle term. If both conclusions contain the middle term ( cakes) neither of them can follow.

Rule 2.

No 'term' can be distributed in the conclusion unless it's distributed in the premises.

Conclusion ' No lamps is bags' has lamps being distributed just like the premise " All lamps are cakes" has lamps being distributed.

Therefore Rule 2 is observed ( meaning we should have a viable conclusion to follow).

Rule 3

The middle term should be distributed at least once in the premises.

Cakes the middle term is not distributed in any of the premises.

And as such, the conclusion cannot follow.

Rule 4, of circumstances under which no conclusion follows, is not applicable because;

a) both premises are particular ( both premises are Universal - All).

b) both premises are negative ( both are Affirmative).

c) major premise is particular and the minor is negative ( both premises are Minor & Positive/Affirmative).

This would suggest we expect to have a conclusion to follow.

Rule 5

If the middle term is distributed twice, the conclusion is universal.

The middle term cakes is not distributed at all.

So, this rule is not applicable.

Rule 6.

The conclusion must be negative if one premise is negative.

Both premises are positive/affirmative.

So this rule is not applicable.

Rule 7,

The conclusion must be Particular if one premise is particular.

Both premises are Universal.

So this rule is not applicable.

In Mathematics, BODMAS is a Standard Rules Guide on which 'rule/procedure' is executed before the other.

If this logical deduction is not subjective (is STANDARD), what is the standard guiding protocol for resolving these logical deductions?

Is it the immediate deductive inference that is considered before the mediate deductive inference or vice versa?

Or is it the Venn diagrams deduction approach that is prime with the other two followings?

Or is it this subjective adoption of the rules as per the person setting these questions?

Anyone please clarify this.

(2)

Diyyah said:
3 years ago

@All.

Why D isn't answer?

Listen to me, You can either apply venn diagram formula or tick cross trick for middle term distribution.

But you need to apply both tricks in case if middle termed is not distributed. Then you need to use venn diagram for validity.

If venn diagram shows the same result, go with D.

But here venn diagram shows different result that whether bag nd lamp box in cake box are intersecting (some lamps are bags) or may be not (no lamp is bag).

That's why the answer is C.

Why D isn't answer?

Listen to me, You can either apply venn diagram formula or tick cross trick for middle term distribution.

But you need to apply both tricks in case if middle termed is not distributed. Then you need to use venn diagram for validity.

If venn diagram shows the same result, go with D.

But here venn diagram shows different result that whether bag nd lamp box in cake box are intersecting (some lamps are bags) or may be not (no lamp is bag).

That's why the answer is C.

Divya said:
3 years ago

Option D is the right answer.

(1)

Khyati mehta said:
3 years ago

I think the answer should be D as we can't conclude whether no bags are lamp or some bags are lamp.

(1)

Namita Naikwadi said:
5 years ago

As per given rules for deriving conclusion from two given premises, rule no. 9 is if both premises are universal, conclusion must be universal. So how can be answer C? I think, it should be D.

Ajit Vishwakarma said:
5 years ago

The case in which all lamps are bags ensures the answer is D. Since all lamps are bags implies that conclusion 1 is not followed for this case.

Shubhangi said:
5 years ago

According to me, The correct answer must be D option.

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