Question

Using the adjacent Venn diagram, find the following set:

A’ ∪ B’

Answer 1

From the diagram we get

U = {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8},

A = {−2, −1, 3, 4, 6}

B = {−2,−1, 5, 7, 8}

C = {−3, −2, 0, 3, 8}

A’ = U – A 

= {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8} – {– 2, – 1, 3, 4, 6}

= {– 3, 0, 1, 2, 5, 7, 8}

B’ = U – B 

= {– 3, – 2, – 1, 0, 1, 2, 3, 4, 5, 6, 7, 8} – {– 2, – 1, 5, 7, 8}

= {– 3, 0, 1, 2, 3, 4, 6}

B ∪ C = {– 2, – 1, 5, 7, 8} ∪ {– 3, – 2, 0, 3, 8}

= {– 3, – 2, – 1, 0, 3, 5, 7, 8}

B ∩ C = {– 2, – 1, 5, 7, 8} ∩ {– 3, – 2, 0, 3, 8}

= {– 2, 8}

A’ ∪ B’ = {– 3, 0, 1, 2, 5, 7, 8} ∪ {– 3, 0, 1, 2, 3, 4, 6}

= {– 3, 0, 1, 2, 3, 4, 5, 6, 7, 8}