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:
2 years 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.
(9)
Reddy said:
3 years ago
The correct answer is A.
(5)
Jvd said:
3 years 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".
(4)
Andrew said:
4 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.
(3)
Divya said:
4 years ago
Option D is the right answer.
(2)
Khyati mehta said:
4 years ago
I think the answer should be D as we can't conclude whether no bags are lamp or some bags are lamp.
(2)
Pratik said:
7 years ago
@All.
Think of this question as a Venn-diagram -A big circle for cakes. Inside cakes, there are two circles - one for bags and one for lamps.
Now there are only two possibilities for how the circles inside are drawn, either the two smaller circles intersect(touch at 1 point or intersect at 2 points) or they don't touch at all.
If they intersect, some lamps are bags (and vice versa). If they don't touch, no lamp is bag (and vice versa). These are the only two possibilities, one of these must occur. Hence, they are complementary.
Think of this question as a Venn-diagram -A big circle for cakes. Inside cakes, there are two circles - one for bags and one for lamps.
Now there are only two possibilities for how the circles inside are drawn, either the two smaller circles intersect(touch at 1 point or intersect at 2 points) or they don't touch at all.
If they intersect, some lamps are bags (and vice versa). If they don't touch, no lamp is bag (and vice versa). These are the only two possibilities, one of these must occur. Hence, they are complementary.
(1)
Namita Naikwadi said:
6 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.
(1)
Akanksha said:
9 years ago
Can anyone tell me why option B is not correct?
Achintya said:
1 decade ago
Middle term is not distributed once so no conclusion can be derived.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers