Logical Reasoning - Logical Deduction - Discussion

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.

All bags are cakes.
All lamps are cakes.

(Venn Diagram Approach).

Draw a rectangle, name it "cakes"
Lamps and bags will come inside this rectangle, right?
Now draw a circle inside the rectangle and name it "bags"

Now for lamps there are two cases,

i.We can draw a circle "lamps" that overlaps with "bags"

ii. We can draw a circle that is disjoint from "bags"

These are the two options. At a time only one can be true right? (Because two circles can never intersect and be disjoint at the same time).

So the answer is Either.

@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.

@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.

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

Means Some lamps may be bags or may not be bags.

If "may be bag" then conclusion "II. No lamp is bag" will not be valid. Conclusion 1 will only valid.

If "may not be bags" then conclusion "I. Some lamps are bags" will not valid. Only conclusion 2 will valid.

So the answer is C] Either I or II follows.

Let us assume that bag=X, cake=Y & lamp=Z, then from d question it is clearly indicated that X=Y & Z=Y, that means some X=Z which is written in conclusion 1.

But it's contrast statement "NO LAMP IS BAG" is written conclusion 2. so i think the option 1 is the right ans. can any one tell

whether i'm right or wrong ?

Cake is the pool, could be composed of bags and lamps only or more.
All bags are part of the pool.
All lamps are also part of the pool.

If some lamp are bags, it makes the second statement invalid and.
If no lamp is a bag, making statement one invalid.

So only one can be the answer, so either.

The answer is C as there are only two possibilities i.e. some lamps are bags or no lamp is a bag. Only one of them has to be correct. One can deduce this using Venn diagram. Option D could have been the correct answer given that the conclusions had one different statement than stated above.

If the middle term is not distributed then how could we drawn any conclusion i.e. the answer must be no conclusion and as far as the given options is concerned the answer must be neither I nor II rather than the either I or II.

Please reply what is the correct answer I'm quiet confused.

All (Universal affirmative statement) bags (+) are cakes (-).

All (Universal affirmative statement) lamps (+) are cakes (-).

Here the middle term is cakes (both are minus). At least one plus (+) should contain to follow the conclusion). So here both are minus. Answer is no conclusion.