1.

Rewrite the given statement with "if then" in five different ways conveying the same meaning1) If p is prime number then sqrtpis an irrational number

Answer»

Solution :r : If p is prime number then `SQRTP`is an irrational number
Above statements r corresponds TOTWO statements p and q
p : p is a prime number
q : `sqrtp` is an irrational number
Then , if p then qis same as the following
(i) p `rArr`q , p is a prime number implies that `sqrtp` is an irrational number
(ii) p is sufficent condition for q
If we lnow that a number p is prime , then it is sufficent to conclude that `sqrtp` is a prime number
p only if q
A number p is prime only if `sqrtp` is an irrational number
(IV) `sqrtp` is an irrational number is NECESSARY conndition for p to be prime
(V) `~q rArr ~p` i.e.,
If `sqrtp` is not an irrational number then p is not a prime number


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