Since the statement is conditional statement ( if....then).

Since for example n = 4 will give LHS as 16 and RHS as 4! = 1.2.3.4= 24

For example , if x = 0 and n > 1 , say n = 2 then the given inequality will become 12 > 1 , which is not true. Hence both the conditions on x and n are needed.

Because the statement is incomplete without the conclusion/ RHS

when n = 2 , L H S : n ! = 2 ! = 2x1 = 2 RHS:

But if n = 1 , the inequation does not hold good.

Replacing n by 1,2,3... we get the expression with the factor ( x - y ).Hence it is divisible by ( x - y ).

If n = 1 then the statement becomes 1x2x3x4= 24 : the consecutive natural numbers when substituted will be multiples of 24.

Since if n = 1 the answer is 2 which is even . also p ( 1 ) = p ( 2 ) is also not true since p(2 ) is 6 which is even.

If n = 0 the given expression becomes 1.2.3.4........r = r! Also when n = 1 one more extra term will be there in the product 2.3.4........which is also divisible by r!.

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Replace n = 1, 2 3 then LHS = RHS