Answer :

(i) Given: A = {-2, 2} and B = {0, 3, 5}

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, 2} and B = {0, 3, 5}. So,


A × B = {(-2, 0), (-2, 3), (-2, 5), (2, 0), (2, 3), (2, 5)}


(ii) Given: A = {-2, 2} and B = {0, 3, 5}


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, 2} and B = {0, 3, 5}. So,


B × A = {(0, -2), (0, 2), (3, -2), (3, 2), (5, -2), (5, 2)}


(iii) Given: A = {-2, 2}


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, 2} and A = {-2, 2}.So,


A × A = {(-2, -2), (-2, 2), (2, -2), (2, 2)}


(iv) Given: B = {0, 3, 5}


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 = {0, 3, 5} and B = {0, 3, 5}. So,


B × B = {(0, 0), (0, 3), (0, 5), (3, 0), (3, 3), (3, 5), (5, 0), (5, 3), (5, 5)}


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