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WebLet A, B and C be sets. Show that (A−B)−C = A−(B ∪C) Proof. (A−B)−C = (A∩Bc)−C set difference = (A∩Bc)∩Ccset difference = A∩(Bc∩Cc) associative = A∩(B ∪C)cde Morgan’s = A−(B ∪C) set difference Proof. Let x ∈ (A − B) − C. Then x ∈ (A − B) and x 6∈C by definition of set difference. Further, x ∈ A and x 6∈B also by definition of set difference. WebThe Cartesian product A × B × C of sets A, B and C is the set of all possible ordered pairs with the first element from A, the second element from B, and the third element from C. This can be represented as: A × B × C = { (1, a, x) : 1 ∈ A, a ∈ B, and x ∈ C} What is the Cartesian product of A (1, 2) and B (a, b)? Given sets are: A (1, 2) B (a, b) slow down mouse
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WebA B=C only when A⊆B B B=C only when A⊆C C B=C D None of these Medium Solution Verified by Toppr Correct option is C) Let xϵB.⇒xϵA∪B⇒xϵA∪C. Case I. xϵA ∴xϵA∩B or xϵA∩C or xϵC ∴B⊆C. Case II. xϵC ∴xϵB⇒xϵC or B⊆C. Similarly C⊆B.∴B=C. Was this answer helpful? 0 0 Similar questions If A={1,2,3,4,5},B={4,5,6,7,8},C={7,8,9,10,11} and … WebApr 18, 2024 · Explanation: The transitive property of equality tells us that if. a = b,b = c, then it follows that a = c. slow down mouse speed