Let the universal set be U = ALL INTEGERS (|Z) (*I will use the symbol (|Z) for
ID: 1719796 • Letter: L
Question
Let the universal set be U = ALL INTEGERS (|Z) (*I will use the symbol (|Z) for Integers here) and consider the sets A, B, C and D where A= {1, 5, 8, 11, 14, 17,...} and B= {n is an element of |Z: n is odd}, and C= {x is an element of |Z: x is not prime}, and D= {1, 2, 3, 5, 8, 13, 21, 34, 55,...}. Which of the following statements are true? Give a complete explanation for each: (#1) 26 is an element of A. (#2) 65 is an element of D. (#3) 100 is not an element of A U D (union). (#4) C Complement (C') is a subset of B. (#5). C intersection B = empty set.
Explanation / Answer
A={1,5.,8,11,14,17,20,23,26,29.....}
B={1,3,5,7,9,11,13,15.......}
C={4,6,8,9,10,12,14,.......}
D={1,2,3,5,8,13,21,34,55......}
#1) 26 is an element because the common difference between the elements is 3.
#2) 65 is not an element of D because the sequence has numbers where the next number is addition of the first two numbers like [1,2,3,5,8,13,21,34,55,89......]
#3) 100 is neither an element of A nor D
#4)C' is subset of B : C is a set of elements which are not prime therefore its complement will have elements which are prime.Set B is a set of odd numbers therefore C' is a subset of B
#5)C intersection B is not empty because C is the set which has the elements which are not prime while B is the set which has odd numbers therefore it will have elements in common
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