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(i) Verify by method of contradicition ...

(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

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(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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