SOLUTION: could any one help me in my homework please =) suppose that S and T both are sets such that T subset of S then show that : a) if S is a finite set ,then T is also finite set.

Question 515378: could any one help me in my homework please =)
suppose that S and T both are sets such that T subset of S then show that :
a) if S is a finite set ,then T is also finite set.
b) if T is an infint set, then S is an infinites set.
waiting your help <3 <3
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
We'll prove (b) first. If T is an infinite set, and T is a subset of S, then S contains an infinite set, and therefore must be an infinite set itself. There are more sophisticated ways to show this, but this is a perfectly reasonable proof.
Now notice that (a) is the contrapositive of (b). Recall that the contrapositive of a statement "if p is true, then q is true" is "if q is not true, then p is not true." Another way to state (a) is "if S is not an infinite set, then T is not an infinite set." So (a) is the contrapositive of (b). Now, we know that if an implication like (b) is true, then its contrapositive is also true, and vice versa. So by proving (b) and showing that (a) is its contrapositive, we have proven (a).
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