Question

Find the union, intersections and the difference ( A – B) of the following pairs of sets.
(a) A= The set of all letters of the word FEAST
B= The set of all letters of the word TASTE
(b) A= {×: × ∈ W , 0 < × ≤ 7}
B= {×: × ∈ W , 4 < × < 9}

Answer 1

Step-by-step explanation:

A) Set A = (F,E,A,S,T)

Set B = (T,A,S,T,E)

UNION :

U = {F,E,A,S,T}

INTERSECTION :

= {T,A,S,E}

DIFFERENCE :

D = {F,T}

B) Set A = {1,2,3,4,5,6}

Set B = {5,6,7,8}

UNION :

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

INTERSECTION :

= {5,6}

DIFFERENCE :

= {1,2,3,4,7,8}

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Answer 2

Step-by-step explanation:

Given:

(a) A= The set of all letters of the word FEAST

B= The set of all letters of the word TASTE

(b) A= {x: x ∈ W , 0 < x ≤ 7}

B= {x: x∈ W , 4 < x< 9}

To find: Find the union, intersections and the difference ( A – B) of the following pairs of sets.

Solution:

Tip: Write roaster form for each set.

(a) A= The set of all letters of the word FEAST

B= The set of all letters of the word TASTE

Step 1:Write sets in roaster form

A={A,F,E,S,T}

B={A,E,S,T}

Step 2: Find Union of both A and B

$A\cup B$={A,E,F,S,T}

Step 3: Write intersection

$A\cap B$={A,E,S,T}

Step 4: Write difference A-B

A-B={F}

(b) A= {x: x ∈ W , 0 < x ≤ 7}

B= {x: x∈ W , 4 < x< 9}

Step 1:Write sets in roaster form

A={1,2,3,4,5,6,7}

B={5,6,7,8}

Step 2: Find Union of both A and B

$A\cup B$={1,2,3,4,5,6,7,8}

Step 3: Write intersection

$A\cap B$={6,7}

Step 4: Write difference A-B

A-B={1,2,3,4}

Final answer:

a)$A\cup B$={A,E,F,S,T}

$A\cap B$={A,E,S,T}

A-B={F}

b)$A\cup B$={1,2,3,4,5,6,7,8}

$A\cap B$={6,7}

A-B={1,2,3,4}

Hope it helps you.

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