Question

If

Solve the following problems and draw Venn diagrams for each of them.

Answer 1

P = {a, b, c, d, e}

Q = {a, e, i, o, u}

R = {a, c, e, g, i}

(1) P ∩ Q = {a, b, c, d, e} ∩ {a, e, i, o, u}

= {a, e}

And the Venn diagram is:

(2) Q ∩ R = {a, e, i, o, u} ∩ {a, c, e, g, i}

= {a, e, i}

And the Venn diagram is:

(3) P ∩ R = {a, b, c, d, e} ∩ {a, c, e, g, i}

= {a, c, e}

And the Venn diagram is:

(4) (P ∩ Q) ∩ R = {a, e} ∩ {a, c, e, g, i} (From (1) P ∩ Q = {a, e})

= {a, e}

And the Venn diagram is:

(5) P ∩ (Q ∩ R) = {a, b, c, d, e} ∩ {a, e, i} (From (2) Q ∩ R= {a, e, i})

= {a, e}

And the Venn diagram is: