Question

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Answer 1

Step-by-step explanation:

Solutions:-

1)Given sets are :

A = {1, 2, 3}

B = {2, 3, 4}

AnB = {1, 2, 3} n { 2,3,4 }

AnB = {2,3}

Now

(AnB) X A

=> { 2,3 } X { 1 , 2, 3 }

=> { (2,1) , (2,2) , (2,3) , (3,1) , (3,2) , (3,3) }

(AnB) X A for the given problem is

{ (2,1) , (2,2) , (2,3) , (3,1) , (3,2) , (3,3) }

2) Given sets are :

A = {1,2,3,4} and B = {a,b,c}

(i)

3)

A = { 1,2,3,4}

B = { 1,2,3}

A×B = { 1,2,3,4}×{1,2,3}

=> {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3)} -------(1)

B×A = {1,2,3}×{1,2,3,4}

=> {(1,1),(1,2),(1,3),(1,4),(2,1)(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4)}----------(2)

From (1)&(2)

A×B ≠ B×A

They are not equal.

4)

Given that (x+1,5) = (4,x+2y)

=> x+1 = 4 and 5 = x+2y

=> x = 4-1

=> x = 3

now

5 = x+2y

=> 5 = 3+2y

=> 5-3 = 2y

=> 2 = 2y

=> 2y = 2

=> y = 2/2

=> y = 1

Therefore, x = 2 and y = 1

5)

Given that

A = {3,4}

B = { 2,3,4}

C ={3,4,5}

BXB = {2,3,4}×{2,3,4}

=> {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4),(4,2),(4,3),(4,4)}

and

CXC = {3,4,5}X{3,4,5}

=> {(3,,3),(3,4,)(3,5),(4,3),(4,4),(4,5),(5,3),(5,4),(5,5)}

Now

(BxB) n(CxC)

=> {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4),(4,2),(4,3),(4,4)} n

{(3,,3),(3,4,)(3,5),(4,3),(4,4),(4,5),(5,3),(5,4),(5,5)}

=> {(3,3),(3,4),(4,3),(4,4,)}

Used formulae :-

• AxB is the Cartesian product of the two sets A and B on which (a,b) form a belongs to A and b belongs to B

• AnB is the set of Common elements in both A and B