Question

If M and N are two sets,U is the universal set , ϕ denotes an empty set and ((M∩U)∪(N∪ϕ))=((M∪ϕ)∩M)∩(N∪N)
then which of the following is(are) true?

1.M or N is an empty set.
2. M=N
3.The cardinality of M∖N is 0.
4.N is proper subset of M

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given : M and N are two sets,U is the universal set , ϕ denotes an empty set and ((M∩U)∪(N∪ϕ))=((M∪ϕ)∩M)∩(N∪N)

To Find : which of the following is(are) true?

Solution:

((M∩U)∪(N∪ϕ))

N∪ϕ = N

=  ((M∩U)∪(N)

M∩U  = M

= M∪ N

((M∪ϕ)∩M)∩(N∪N)

N∪N = N

M∪ϕ = M

(M∩M)∩(N)

M∩M = M

M ∩ N

M ∪ N = M ∩ N

=> M = N

Hence  M = N is true

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