While A B C D is the Cartesian product of A and the Cartesian product of B and

While a b c d is the cartesian product of a and the

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product of and D. While A × (B × C) × D is the Cartesian product of A and the Cartesian product of B and C and finally the Cartesian product of D. In more simple terms, (A × B) × (C × D) is (a,b) x (c,d) while A × (B × C) × is (a) x (b,c) x (c) 42) a) There exists some x in the domain of reals such that x^3 = -1. This is true because x = -1 b) There exists some x in the domain of integers such that x+1>x. This is true because x = 1 c) For all x in the domain of integers, x- 1 is contained in the domain of integers. This is true because any integer minus 1 (another integer) is still an integer. d) For all x in the domain of integers, x^2 is contained in the domain of integers. This is true because any integer squared (times itself) is still an integer. 2.2 2)
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a) A∩B b) A- B c) A B d) A’ B’ 4) a) {a,b,c,d,e,f,g,h} b) {a,b,c,d,e} c) { } d) {f,g,h} 18) a) From the definition of union, A B is a subset of A B C because A B is in A B C b) This should be false because every element of (A ∩ B ∩ C) is not in (A ∩ B) 26) a) b) c) 32) {2, 4} 48) a) {1,2,3, . .. , n} b) {1} 50)
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52) a) 0011100000 b) 1010010001 c) 0111001110 54) a) A subset of x that contains no x b) A subset of x that is included each position in x
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