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ID: 3111155 • Letter: V
Question
Vivian is a mathematician, so she means exactly what she says. She says "I'm going to the zoo only if it doesn't rain". Check all logically equivalent forms of this statement: 1) If it rains, Vivian will not go to the zoo. 2) if it doesn't rain, Vivian will go to the zoo. 3) If Vivian is going to the zoo, then it is not raining. 4) If Vivian is not going to the zoo, it is raining. Vivian is a mathematician, so she means exactly what she says. She says "I'm going to the zoo only if it doesn't rain". Check all logically equivalent forms of this statement: 1) If it rains, Vivian will not go to the zoo. 2) if it doesn't rain, Vivian will go to the zoo. 3) If Vivian is going to the zoo, then it is not raining. 4) If Vivian is not going to the zoo, it is raining. 1) If it rains, Vivian will not go to the zoo. 2) if it doesn't rain, Vivian will go to the zoo. 3) If Vivian is going to the zoo, then it is not raining. 4) If Vivian is not going to the zoo, it is raining.Explanation / Answer
Correct options:
(1) If it rains, Vivian will not go to the zoo.
(3) If Vivian is going to the zoo, then it is not raining.
EXPLANATION:
Let
A = I am going to zoo (1)
B = It does not rain. (2)
By definition:
A only if B means that A can only ever be true when B is true. (3)
Substituting (1) and (2) respectively for A and B in the definition (3), we get:
I am going to zoo only if it does not rain means that I am going to zoo can ever be true when It does not rain is true.
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