Determine whether the following statements are true or false. a) If {1} is an el

Question

Determine whether the following statements are true or false.  

a) If {1} is an element of the power set P(A), then 1 is an element of A but {1} is not an element of A.

b) If A, B and C are sets such that A is a subset of the powerset P(B) which is also a subset of C and |A|=2, then |C| can be 5 but |C| cannot be 4.

c) If a set B has one more element than a set A, then the power set P(B) has at least two more elements then the power set P(A).

d) If four sets A, B, C and D are subsets of {1,2,3} such that |A|=|B|=|C|=|D|=2, then at least two of these sets are equal.

Explanation / Answer

a) false, if {1} is an element of power set of A then {1} must be a element of A.

b)false, |C| can have any number of elements more than 2

c)true, because the power set is a power of 2,let |A| be minimum ie 1 then power set of A has two elements and B will have more than 1 elements so power set of B will have more than 4 elements so the power set P(B) has at least two more elements then the power set P(A).

d) true because we can make a number of different sets from {1,2,3} that has 2 elements and that is 3C2 ie 3

and here we are making four so atleast two sets must be equal

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