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1. Use Truth Table to show (-9^(-&gt;VVq)) p is always True. 2. Lecture Note Problem 5: Prove that for any two sets A and B: A-B = B-A A=B 3. Prove that for any sets A, B and C the following identities hold: a) A-(B-C)=(A-B)O(AnC). b) A-(BnC)=(A-B)O(A-C). 4. [Symmetric Difference] Prove that the following identities are equivalent: a) and b) B=C . (08) Prove or disprove: (a)(A-B)-C(A-C)-(B-C). - - - (b) A -(B-C)=(A-B)-C. - - - (21) Let a,beR with a<b. we="" define="" four="" kinds="" of="" intervals:<br="">[this is an open interval] [this is a closed interval] [this is a "half open-half closed" interval] [a,6)=(xeR(asxeb) [this also is a "half open-half closed'interval] Calculate the following unions and intersections: (a) (b) Ue,1] (c) Ut,1,1) (d) U 1,1) n=1 n=1 * (e) n [0,2] [0,2) (g) n (0,1] (h) n n=1 n=1 n=1 m=2 </b.>(24) Prove or disprove: for any two sets A,B:P(AB)=P(A)nP(B).

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