Please answer last three question e,c,d You are given the set A - [a, b, c} Find
ID: 3113008 • Letter: P
Question
Please answer last three question e,c,d
You are given the set A - [a, b, c} Find all subsets of the set A (that is, find the power set of A) Is the power set of A a partition of A? If not, why not? Find all partitions of the set A For each partition of A, create the relation induced by the partition. For each relation, find [a]_R-[b]_R [c]_R = what partition of A' = {a, b, c, d) creates the equivalence relation with the fewest elements? 8d, what partition of A' = {a, b, c, d) creates the equivalence relation with the most elements?Explanation / Answer
Ans(8.a):
Power Set of set {a,b,c} is given by:
P(A) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} }
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Ans(8.b):
partition of a set doesn't include empty set { } and no element overlaps other.
We can see that Power set contains empty set. Hence power set of A is NOT partition of A.
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Ans(8.c):
partition of set A is given by:
{a,b,c}={{a,b},{c}}
{a,b,c}={{a,c},{b}}
{a,b,c}={{c,b},{a}}
{a,b,c}={{a},{b},{c}}