1.

(i) Verify by method of contradicition p : There are infinitely many numbers (ii) Verify by method of contradicition p : If p and q are rational number q ne 0 and r is an irrational number, then p+qr is irrational

Answer»

Solution :(i) Let us assume that there are only FINITELY many primes ,`p_1,p_2,……….p_n`
Now contructing a number
`p=p_1xxp_2xxp_3xx….xxp_(n+1)`
CLEARLY , p is larger than all primes. So it is not divisble by any existing prime . So, according to defination of prime number p is true . So our ASSUMPTION is wrong
So, given statement is true
(ii) Let us assume that
p+qr is irrational
so, qr is irrational
so, `(qr)/q=r` is RATIONAL , which contradicts
so, p is true


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