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The contra positive of the statement, if x is a prime number and x divides ab, then x divides a or x divides b, can be symbolically represented using logical connectives on appropriately defined statements p, q, r and s as

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$(~ r \lor ~ s) \to (~ p \land ~ q)$

$(r \land s) \to (~ p \land ~ q)$

$(~ r \land ~ s) \to (~ p \lor ~ q)$

$(r \lor s) \to (~ p \lor ~ q)$

answer is C.

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Detailed Solution

$Let p = x is prime number q = x divides a b r = x divides a$

$s = x divides b The given statement becomes in logical form is p \land q \to r \lor s I t' s c o n t r a p o s i t i v e i s$

$\begin{array}{l} ~ (r \lor s) \to\sim (p \land q) \\ \Rightarrow (~ r \land ~ s) \to (~ p \lor ~ q) \end{array}$

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