Question

Which of the following statements are true and which are false?

(i) The sum of two odd numbers is an odd number.
(ii) The sum of two odd numbers is an even number.
(iii) The sum of two even numbers is an even number.
(iv) The sum two even number is an odd number.
(v) The sum of an even number and an odd number is an odd number.
(vi) The sum of an odd number and an even number is an even number
(vii) Every whole number is a natural number.
(viii) Every natural number is a whole number.
(ix) There is a whole number which when added to a whole number, gives that number.
(x) There is a natural number which when added to a natural number, gives that number.
(xi) Commutativity and associativity are properties of whole numbers.
(xii) Commutativity and associativity are properties of addition of whole numbers.

Answer 1

(i) FALSE ( 3 + 5 = 8; 8 is an even number.)
(ii) TRUE (3 + 5 = 8; 8 is an even number.)
(iii) TRUE (2 + 4 = 6; 6 is an even number.)
(iv) FALSE (2 + 4 = 6; 6 is an even number.)
(v) TRUE (2 + 3 = 5; 5 is an odd number.)
(vi) FALSE (3 + 2 = 5; 5 is not an even number.)
(vii) FALSE [The whole number set is {0, 1, 2, 3, 4,...), whereas the natural number set is {1, 2, 3, 4,...).]
(viii) TRUE [The whole number set is {0, 1, 2, 3, 4,...), whereas the natural number set is {1, 2, 3, 4,...).]
(ix) TRUE [That number is zero.]
(x) FALSE
(xi) FALSE
(xii) TRUE