Question

using Venn diagram prove that for the sets x,yand z. (x-y) - z = x -( y intersection z)​

Answer 1

Let me correct the question first.

It should be: (X - Y) - Z = X - (Y ∪ Z)

Step-by-step explanation:

Refer to the attachment.

Left hand side

1. First draw X - Y. To find X - Y, shade the part of X, where Y is not.
2. Then draw (X - Y) - Z. Shade the part of X - Y, where Z is not.

Right hand side

1. First draw Y ∪ Z. To find Y ∪ Z, shade the whole of Y and Z.
2. Then draw X - (Y ∪ Z). Shade the part of X, where Y ∪ Z is not.

Hence proved using Venn diagrams.

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