Let set A = {x : x ∈ Z and x² - 9 = 0} and set B = {x : x ∈ W and x² - 16 < 0}; then find :

(i) A ∪ B

(ii) B ∩ A

Set A = {x : x ∈ Z and x² - 9 = 0}

x² - 9 = 0

x² = 9

x = $\sqrt{9}$

x = 3 or -3

Set A = {-3, 3}

Set B = {x : x ∈ W and x² - 16 < 0}

x² - 16 < 0

x² < 16

x < $\sqrt{16}$

x < 4

Set B = {0, 1, 2, 3}

(i) A ∪ B

A ∪ B - contains all the elements of set A and B.

A ∪ B = {-3, 3} ∪ {0, 1, 2, 3}

A ∪ B = {-3, 0, 1, 2, 3}

(ii) B ∩ A

B ∩ A - contains all the common elements in set B and A.

B ∩ A = {0, 1, 2, 3} ∩ {-3, 3}

B ∩ A = {3}