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38. Consider three sets \( X, Y \) and \( Z \) having 6,5 and 4 elements respectively. A.11 these 15 elements are distinct. Let \( S=(X-Y) \cup Z \). How many proper subsets does \( S \) have?(a) 255(b) 256(c) 1023(d) 1024 |
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Answer» Given : n(X)=6 n(y)=5 n(z)=4 Also,the elements are distinct Therefore,these three are disjoint sets ==>n(X∩Z) =0 -------- (1) Now,her S=(X-Y)∪Z=X∪Z [Because X∩Z=∅==>X-Z=X] ==>n(S)=n(X∪Z) ==>n(S)=n(X)+n(Z)-n(X∩Z) ==>n(S)=n(X)+n(Z)-0 [From (1)] ==>n(S)=6+4=10 Therefore, Number of proper subsets of S=2n(S)-1 =210-1 =1024-1=1023 Hence,the correct answer is option (c)1023 |
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