Question

 If X and Y are two sets, then X⋂(Y⋃X) C equals

(a) X (b) Y (c) ϕ (d) None of these 

My attempt:

X = {1,2,3} Y = {3,4,5}

(Y⋃X) = {1,2,3,4,5}

X⋂(Y⋃X) = {1,2,3}

But the given answer is C

Comments

@Prasanna 

 Here X$\cap$(Y$\cup$ X) C 

means ${(X\cap(Y\cup X))}'$  or it means X$\cap$${(Y\cup X)}'$

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Thanks Sir. I didn't see that C as "Complement"

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see this...

Answer 1

X ⋂ (Y ⋃ X)' = X ⋂ (Y' ⋂ X') =  ϕ

Answer 2

just convert to boolean expression and solve by digital logix. like

x . ( y+x)' = x.( y' . x')

now x and x' = 0 so answer will be C