Question

Verify that whether the following is an infinite or not

1.(Z,+)≤(Q,+)
2.(Q,+)≤(R,+)
3.(Z,+)≤(R,+)
4.(Z−{0},)≤.(R−{0}.

Answer 1

To verify whether the given statements are infinite or not, we need to understand the concept of order and the properties of the given sets.

Step-by-step explanation:

To verify whether the given statements are infinite or not, we need to understand the concept of order and the properties of the given sets.

1. (Z,+) ≤ (Q,+): This statement is infinite since the set of integers (Z) is a subset of the set of rational numbers (Q), and both sets are infinite.
2. (Q,+) ≤ (R,+): This statement is also infinite since the set of rational numbers (Q) is a subset of the set of real numbers (R), and both sets are infinite.
3. (Z,+) ≤ (R,+): This statement is infinite since the set of integers (Z) is a subset of the set of real numbers (R), and both sets are infinite.
4. (Z−{0},) ≤ (R−{0}): This statement is infinite since the set of non-zero integers (Z−{0}) is a subset of the set of non-zero real numbers (R−{0}), and both sets are infinite.