SET 1. Suppose that A, B, and C are sets. Prove or disprove that (A-B) _ C = (A-
ID: 3670310 • Letter: S
Question
SET 1. Suppose that A, B, and C are sets. Prove or disprove that (A-B) _ C = (A-C)--B 2. The symmetric difference of A and B is the set containing those elements in either A or B, but not in both A and B. Find the symmetric differences of 1, 3, 5 and {1, 2, 3} 3. Show the Power Set of {A, B, C, D, E) LOGIC 4. Show that _(p v-q) and q /-p are equivalent (a) Using a truth table (b) Using logical equivalence A compound proposition is satisfiable if there is an assignment of truth values to the variables in the proposition that makes the compound proposition true. Is the following compound propositions is satisfiable? 5. 6. Use De Morgan's laws to write negations for the following statements Hal is Math major and Hal's sister is a CS major a. b. The connector is loose or the machine is unplugged Determine whether the statements in (a) and (b) are logically equivalent: a. Bob is majoring in both Math and CS, and Ann is majoring in Math but Ann 7. is NOT majoring in both Math and CS b. It is NOT the case that Bob and Ann are majoring in both Math and CS, but it is the case that Ann is majoring in Math and Bob is majoring in both Math and CS 8. Use Theorem of Logical Equivalence to verify the following. Supply a reason for each stepExplanation / Answer
1. (A-B)-C =(A-C)-(B-C)
=(A-C)-B
2. The symmetric difference between the sets {1, 3, 5} and {1, 2, 3} is {2, 5}. Since 2, 5 elements are each in one set, but not both in the sets.
3. Power Set have five elements. So, Power Set should contain 2^5 = 32 items. Each subset term starting at 0 through 32 - 1 = 31.
Power set P = {{}, {A}, {B}, {C}, {D}, {E}, {A,B}, {A,C}, {A,D}, {A,E}, {B,C}, {B,D}, {B,E}, {C,D}, {C,E}, {D,E}, {A,B,C}, {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E}, {A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, {C,D,E}, {A,B,C,D}, {A,B,C,E}, {A,B,D,E}, {A,C,D,E}, {B,C,D,E}, {A,B,C,D,E }}
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