Prove abN a b not equal to 0 Hint Prove the statement by ind

Prove a,bN a· b not equal to 0.

Hint: Prove the statement by induction with respect to b.

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a,b belongs to N.

This implies a and b must be +ve numbers.

The product of two +ve natural number can never be zero. So, a.b not equal to zero.

a x b = ab (+ve number). -----(1)

Mathematical induction:

Let a=1 and b=2, then a x b= 1 x 2= 2 (not equal to 0).

To prove its true for b+1 also:

a (b+1) = ab + a

Now, ab is +ve from equation (1). and a belongs to N(+ve). So, the sum of two positive natural numbers is +ve.

Hence proved, a(b+1) is not equal to zero.