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84. Following are given
(i) All P are Q.
(ii) No Q is R.
From (i) and (ii) we can infer that
(a) some P are R
(b) no P is R
(c) all P are R
(d) None of the above
Proof: Statement (i) says that P is a subset of Q.
Statement (ii) says that Q is a subset of R-complement.
Thus, P is a subset of R-complement.
Alternatively,
Story Proof: Let P be the set of people who are good at probability. Let Q be the set of people who have good quantitative skills. Let R be the set of people who are retarded. Clearly, no person who is good at probability is retarded.
Hence, no P is R.
85. Following are given :
(i) Some P are Q.
(ii) No R is Q.
From (i) and (ii) we can infer that
(a) some P are R
(b) no P is R
(c) all P are R
(d) None of the above
Proof: Statement (i) says that P ∩ Q is non empty.
Statement (ii) says that R is a subset of Q-complement.
Clearly none of (a), (b) and (c) can be inferred.
For example:
Example 1: P = {1, 2, 3}, Q = {3, 4, 5}, R = {6, 7, 8} rules out (a) and (c)
Example 2: P = {1, 2, 3}, Q = {3, 4, 5}, R = {1, 6, 7, 8} rules out (b) and (c)
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