Let the statement S be defined as follows, where n is some particular number ind
ID: 3877934 • Letter: L
Question
Let the statement S be defined as follows, where n is some particular number inder discussion: S: "If n is prime, then n is odd or n is equal to 2." Assuming that S is true1 which of the following must also be true? Justify your answers. Use the words converse, inverse, contrapositive, and negation when possible. (a) If n is odd or n is equal to 2, then n is prime. (b) If n is neither odd nor equal to 2, then n is not prime. (c) n is prime only if it is odd or equal to 2 (d) n is not prime unless it is odd or equal to 2. (e) If n is not prime, then it is neither odd nor equal to 2. (f) n is prime and neither odd nor equal to 2 (g) A necessary condition for n to be prime is that it is odd or equal to 2. h) A sufficient condition for n to be prime is that it is odd or equal to 2.Explanation / Answer
Ans : )
Converse : (a) If n is odd or n is equal to 2, then n is prime.
Inverse : (e) If n is not prime, then it is neither odd nor equal to 2.
Contrapositive : (b) If n is neither odd nor equal to 2, then n is not prime.
Negation : (d) n is not prime unless it is odd or equal to 2.
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