Q. 44.8( 4 Votes )

If A = {2, 3, 5}

Answer :

(i) Given: A = {2, 3, 5} and B = {5, 7}

To find: A × B


By the definition of the Cartesian product,


Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.


P × Q = {(p, q) : p Є P, q Є Q}


Here, A = {2, 3, 5} and B = {5, 7}. So,


A × B = (2, 3, 5) × (5, 7)


= {(2, 5), (3, 5), (5, 5), (2, 7), (3, 7), (5, 7)}


(ii) Given: A = {2, 3, 5} and B = {5, 7}


To find: B × A


By the definition of the Cartesian product,


Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.


P × Q = {(p, q) : p Є P, q Є Q}


Here, A = {2, 3, 5} and B = {5, 7}. So,


B × A = (5, 7) × (2, 3, 5)


= {(5, 2), (5, 3), (5, 5), (7, 2), (7, 3), (7, 5)}


(iii) Given: A = {2, 3, 5} and B = {2, 3, 5}


To find: A × A


By the definition of the Cartesian product,


Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.


P × Q = {(p, q) : p Є P, q Є Q}


Here, A = {2, 3, 5} and A = {2, 3, 5}. So,


A × A = (2, 3, 5) × (2, 3, 5)


= {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)}


(iv) Given: B = {5, 7}


To find: B × B


By the definition of the Cartesian product,


Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.


P × Q = {(p, q) : p Є P, q Є Q}


Here, B = {5, 7} and B = {5, 7}. So,


B × B = (5, 7) × (5, 7)


= {(5, 5), (5, 7), (7, 5), (7, 7)}


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