Question

5 marks question long answer type

dont spam

solve all the numbers​

Answer 1

Answer:

Replace A and B with X and y

(i)X∪ Y = {x | x ∈ X or x ∈ Y} Thus x ∈ Y ⇒ x ∈ X ∪ Y Hence, Y ⊂ X ∪ Y

(ii)X ∩ Y = {x | x ∈ X and x ∈ Y}

Thus x ∈ X ∩ Y ⇒ x ∈ X HenceX ∩ Y ⊂ X

X ∩ Y = {x | x ∈ X and x ∈ Y}

Thus x ∈ X ∩ Y ⇒ x ∈ X HenceX ∩ Y ⊂ X

Note that

(iii) x ∈ X ∩ Y ⇒ x ∈ X ThusX ∩ Y ⊂ X Also, sinceX ⊂ Y,

x ∈ X ⇒ x ∈ Y ⇒ x ∈ X ∩ Y so thatX ⊂ X ∩ Y

Hence the result X = X ∩ Y follows.