State the following statement is True or False
If x, y, and z are prime numbers and x < y < z and xy is even, then the value of x is even.

True

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False

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Solution

The correct option is A True
If xy is even, then x is even or y is even. Since x < y, x must equal 2, because 2 is the smallest and only even prime number.

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x y

z

(x + z)

Check whether the following ststement are true or not :

(i) p : If x and y are odd integers, then x + y is an even integer.

(ii) q : If x, y are integers such that xy is even, then at least one of x and y is an even integer.

State whether the following statements are True or False:

(a) The sum of three odd numbers is even.

(b) The sum of two odd numbers and one even number is even.

(d) If an even number is divided by 2, the quotient is always odd.

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

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