Prove that if x is odd, then `x^2` is also odd

p : x is odd , q : x^(2) is odd. The symbolic form of "If x is odd then x^(2) is odd", is

p : x is odd , q : x^(2) is odd. The symbolic form of "If x is not odd then x^(2) is odd", is

Check whether the following statement is true or false by proving its contrapositive. If x, y in Ζ such that xy is odd, then both x and y are odd.

Check whether the following statement is true or not. Id x, y in Z are such that x and y are odd, then xy is odd.

p : x is odd , q is x^(2) is odd. The symbolic form of " x is odd and x^(2) is not odd", is

p : x is odd, q : x^(2) is odd. The symbolic form of "x is odd iff x^(2) is odd", is

p : x is odd , q : x^(2) is odd. The symbolic form of" x is odd or x^(20 is odd", is

Write the contrapositive and converse of the following statements. If x is a prime number, then x is odd.

Prove that f (x) = x |x| is differentiable at x =0 and find f'(0) also find f '(x) on R.