SRCC GBO 2010 Question Paper

The possible valid conclusions for 'All soaps are oils' can be: 'All soaps are oils, and vice versa', 'All soaps are oils, and not vice versa'.

The possible valid conclusions for 'All oils are bottles' can be: 'All oils are bottles, and vice versa', 'All oils are bottles, and not vice versa'. 

Now, the aim shall be to try and negate each option, and see if any option will hold true in each case (formed by combining any of the two cases). 

1) This is a valid conclusion as it will hold true in any of the cases.

2) This is an invalid conclusion, which can be negated by the case 'All soaps are oils, and not vice versa'.

3) This is a valid conclusion as either all the three elements will coincide (soap, oil, bottle), or soap will be the smallest concentric circle out of the three. 

4) This is an invalid conclusion, which can be negated by the case 'All oils are bottles, and not vice versa'.

The possible valid conclusions for 'Some glasses are kettles' can be: 'Some glasses are kettles, and some kettles are glasses', 'All glasses are kettles, and vice versa', and 'All kettles are glasses, but not vice versa'. 

The possible valid conclusions for 'All kettles are jugs' can be: 'All kettles are jugs, and vice versa', and 'All kettles are jugs, but not vice versa'.

On examining the options, only the first option would hold true irrespective of whichever two statements we combine. In order to arrive at the correct answer, we shall try negating each option by finding a case that invalidates the conclusion. If we find a conclusion that holds true in every possible combination, it happens to be a va;id one. For example, the third conclusion gets invalidated when we combine 'All glasses are kettles, and vice versa', and  'All kettles are jugs, and vice versa'.

Following are the possible conclusions of 'Some dogs are cats': 'Some dogs are cats, and vice versa', 'All dogs are cats, and vice versa', 'All dogs are cats, and not vice versa'. 

Following are the possible conclusions of 'Some tigers are cats': 'Some tigers are cats, and vice versa', 'All tigers are cats, and vice versa', 'All tigers are cats, and not vice versa'.

We shall now eliminate each of the options which is not a universal conclusion based on the given premises. The conclusions which will hold true everytime will be our answer. 

1.  Every cat is either a dog or a tiger.: There is nothing that states that each of the cats falls definitely within one of the sets (dog or tiger). Hence, an invalid conclusion as not universal in nature. 

2 and 3: Some dogs are tigers and No tiger is a dog: These two shall be the only possible cases, and hence one of them shall be true everytime. 

4. Some cats are dogs as well as tigers: We are not sure whether there are cats who fall in the intersection of dogs and tigers. Hence, an invalid conclusion.

Possible valid conclusions from 'All books are magazines' are: 'All books are magazines, and vice versa', 'All books are magazines, but not vice versa'.

Possible valid conclusions from 'All newspapers are magazines' are: 'All newspapers are magazines, and vice versa', 'All newspapers are magazines, but not vice versa'.

The aim now is to eliminate options by finding a combination of possible conclusions that invalidate the said option. 

1) This is true in each of the cases laid down in 'All books are magazines'.

2) The same logic used for the first option, and hence a valid conclusion.

3) This may not be the case, as there is no statement to indicate that each of the elements in 'magazine' has been covered by either a book or newspaper. What if magazine is a way bigger set and 'books/newspaper' form very small sets of the same?

4) Again, it is possible that magazine is a way bigger set and 'books/newspaper' form very small sets of the same. Hence, an invalid conclusion.

Following are the possible conclusion of 'Some pistols are guns': 'Some pistols are guns, and vice versa', 'All pistols are guns, and vice versa', 'All pistols are guns, and not vice versa'.

Following are the possible conclusions of 'Some pistols are swords': 'Some pistols are swords, and vice versa', 'All pistols are swords, and vice versa', 'All pistols are swords, and not vice versa'.

We shall try to find a scenario when the options won't hold true, and if there is an option which is always true, that is a valid conclusion. 

1. Some guns are swords: This can be a valid conclusion in case where there is an intersection between guns and swords.

2. No gun is a sword: This can be a valid conclusion where there is no intersection between the two sets. 

However, we shall note that the two conclusions discussed above cannot happen simultaneously but one of them will definitely occur. 

3.  Every pistol is either gun or sword: This can be negated as there is nothing to state that each of the pistol definitely comes under one other set. 

4. Some pistols are neither gun nor sword: This can be negated as there is nothing to state that there are pistols that fall out of the range of the other two sets. There can be an instance when every pistol is either gun or sword.

Interpreting the statements, we get: N<W, L>N, K=L, W=D

To check 1, we have: N<W and L>N. From this, we cannot conclude that L=W as we cannot derive anything from the magnitude sign.

To check 2, we have: N<W and W=D. On combining these two, we can say that D>N, as N is less that W, which in turn is equal to D. Hence, a valid conclusion.

The following are the expressions: L>A or L=A, S<E, A=S, G>L

To test each of the conclusions:

1. A<E: Since A=S and S<E, it is clear that A<E.

2. G>A: Since G>L, and L>A or L=A, it is clear that G>A.

Following are the interpretations: M=I, A>M, T<I or T=I, T=K

To test each of the conclusions:

1. M=K: Since M=I, T<I or T=I, and T=K, we cannot be sure whether T<I or T=I. THis will only hold true when T=I.

2. K<M: This will only hold true when T<I. 

Hence, either of these shall be true. 

Following are the interpretations: I<R or I=R, D<I, E=C, and R>E.

1. R>C: Since R>E and E=C, it is clear that R>C.

2. I=R: We cannot be sure of this relation. 

Following are the interpretations: U>N, S>Q or S=Q, N<D, and Q=U

1. N<S: Since Q=U, Q>N. Now, S has to be greater than or equal to Q. Hence, N<S.

2. U=D: Since U>N, and N<D, we cannot be sure about the relation between U and D.