Question

2.2 Set
(g) 3€ Q.
(h) {3} C P (Q).
(i) {3} E P(Q).
(i) {{3}} CP(Q).
(k) {3} CQ.
(1) {{3}} € P(Q).
Let A and B be sets. Prove that A = B iff P (A) = P (B).
Assign a grade A (correct), C (partially correct), or F (failur
assignments of grades other than A.
(a) Claim. If X= {XE N: x2 < 14} and Y= {1,2,3},
“Proof.” Since 12 =1 <14, 22 = 4 < 14, and 32 =
(b) Claim. If A, B, and C are sets, and A C B and BC
"Proof.” Let A = {1,5,8), B = {1, 4, 5, 8, 10), a
6, 8, 10}. Then A CB, and B CC, and ACC
(c) Claim. If A, B, and C are sets, and A C B and BC
"Proof.” Suppose x is any object. If x E A, then.
If x e B, then x e C, since B CC. Thus, x E C. The
(d) Claim. If A, B, and C are sets, and A C B and B
"Proof.” If x e C, then, since B CC, XE B. Sing
it follows that x E A. Thus x e C implies X E A. Th
(e) Claim. If A, B, and C are sets, and A C B and B​

Answer 1

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