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(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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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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