Question

Let X = {2, 4, 5, 6} Y = {3, 4, 7, 8} Z = {5, 6, 7, 8}, find

(a) (X - Y) ∪ (Y – X) (b) (X - Y) ∩ (Y - X)

(c) (Y - Z) ∪ (Z – Y) (d) (Y - Z) ∩ (Z – Y)​

Answer 1

ANSWER

(2,3,5,6,7,8)

Step-by-step explanation:

1. first we have to cancel the same element in the both side.
2. And then write the first one
3. (2,5,6)U(3,7,8)
4. JOIN the elements together
5. the answer will get

Answer 2

Therefore the answers are

(a)  {,2,5,6,3,7,8}         (b)  {}

(c) {3,4,5,6}                 (d)   {}

Given:

X = {2, 4, 5, 6}, Y = {3, 4, 7, 8}, Z = {5, 6, 7, 8}

To find:

(a) (X - Y) ∪ (Y – X)     (b) (X - Y) ∩ (Y - X)

(c) (Y - Z) ∪ (Z – Y)      (d) (Y - Z) ∩ (Z – Y)​

Solution:

Given X = {2, 4, 5, 6},  Y = {3, 4, 7, 8},  Z = {5, 6, 7, 8}  

(a) (X - Y) ∪ (Y – X)    

⇒ (X - Y) = {2, 4, 5, 6} -  {3, 4, 7, 8} = { 2, 5, 6}

⇒ (Y – X) = {3, 4, 7, 8} - {2, 4, 5, 6} = {3, 7, 8}

⇒ (X - Y) ∪ (Y – X)  =  {2,5,6,3,7,8}

(b) (X - Y) ∩ (Y - X) =  { 2, 5, 6} ∩ {3,7,8} = {2,5,6,3,7,8}

⇒ (X - Y) ∩ (Y - X) = {}

(c) (Y - Z) ∪ (Z – Y)  

(Y – Z) = {3, 4, 7, 8} – {5, 6, 7, 8} = {3,4}

(Z – Y) =  {5, 6, 7, 8} – {3, 4, 7, 8} = {5,6}

⇒ (Y - Z) ∪ (Z – Y)  =  {3,4,5,6}

(d) (Y - Z) ∩ (Z – Y) =​ {3,4} ∩ {5,6} =  {}

⇒  (Y - Z) ∩ (Z – Y) = {}

Therefore the answers are

(a) (X - Y) ∩ (Y - X) = {,2,5,6,3,7,8}

(b) (X - Y) ∩ (Y - X) = {}

(c) (Y - Z) ∪ (Z – Y)  =  {3,4,5,6}

(d) (Y - Z) ∩ (Z – Y) = {}

#SPJ2