2 Suppose that the universe of discourse is the set of all i

2) Suppose that the universe of discourse is the set of all integers. Let S = {1, 2, 3, 4}. Consider the statement (*) below. (*) x S y (not) S, x > y.

a) Is the statement below true or false? Justify your answer. Include in your justification a discussion of the meaning of the statement. x (not) Sy S, x y

b) Is the statement below true or false? Justify your answer. Include in your justification a discussion of the meaning of the statement. x S y (not) S, x y.

c) Is the statement in a) or in b) or neither equivalent to the negation of (*)? Justify your answer.

Solution

a) true, as according to given statemnt x>y is true, in our problem variables are just reversed so that means y>x is true,it means y>=x is true.

meaning of statement- there exist a element in S which is greater or equal than all other integer not present in S.

b) false, as there exist x for y not belonging to S such that x>y. but this statement exact opposes. it say if you take any x belonging to S, it cant be greater than y not belonging to S.

c) C is the negation. it completely reverses the general statemnt.