Let B be a subset of a set A and let P(A:B)={X E P(A):X is a superset of B} - Maths - Sets

Question

Let B be a subset of a set A and let P(A:B)={X E P(A):X is a
superset of B}
1)show that :P(A: Φ) =P(A)
2)if A={a,b,c,d} and B={a,b} List all the members of the set
P(A:B)

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

1PA:B=X∈PA: X is a superset of B=X∈PA: B is a subset of X=Set of all those subsets of A which contain BPA:ϕ=Set of all those subsets of A which contain ϕ=Set of all subsets of A=PA2A=a,b,c,d  , B=a,bPA:B=Set of all those subsets of A which contain B=a,b , a,b,c , a,b,d , a,b,c,d
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Let B be a subset of a set A and let P(A:B)={X E P(A):X is a superset of B}. 1)show that :P(A: Φ) =P(A) 2)if A={a,b,c,d} and B={a,b}.List all the members of the set P(A:B).

Let B be a subset of a set A and let P(A:B)={X E P(A):X is a superset of B}.

1)show that :P(A: Φ) =P(A)

2)if A={a,b,c,d} and B={a,b}.List all the members of the set P(A:B).