Question 19 Let A be the set of all subsets of the set {C,A,R,D,S} and B be the set of all...
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Let A be the set of all subsets of the set {C,A,R,D,S} and B be the set of all subsets of the word {S,U,R,E}. How many elements does the set A intersect B contain?
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Answer: B. B) 4
The intersection of sets {C,A,R,D,S} and {S,U,R,E} is {R,S}, containing 2 elements. The intersection of their power sets is the power set of {R,S}, which has 2^2 = 4 elements.
Step-by-step Derivation:
Step 1: Let S1 = {C,A,R,D,S} and S2 = {S,U,R,E}.
Step 2: Common elements S1 intersect S2 = {R, S}, so |S1 intersect S2| = 2.
Step 3: For power sets, P(S1) intersect P(S2) = P(S1 intersect S2).
Step 4: Number of subsets = 2^|S1 intersect S2| = 2^2 = 4.