Q. 145.0( 1 Vote )

Let A = {–3, –1},

Answer :

(i) Given: A = {-3, -1} and B = {1, 3}

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 = {-3, -1} and B = {1, 3}. So,


A × B = {-3, -1} × {1, 3}


= {(-3, 1), (-3, 3), (-1, 1), (-1, 3)}


(ii) Given: C = {3, 5}


From part (i), we get A × B = {(-3, 1), (-3, 3), (-1, 1), (-1, 3)}


So,


(A × B) × C = {(-3, 1), (-3, 3), (-1, 1), (-1, 3)} × (3, 5)


= (-3, 1, 3), (-3, 1 , 5), (-3, 3, 3), (-3, 3, 5), (-1, 1, 3), (-1, 1, 5), (-1, 3, 3), (-1, 3, 5)}


(iii) Given: B = {1, 3} and C = {3, 5}


To find: B × C


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 = {1, 3} and C = {3, 5}. So,


B × C = (1, 3) × (3, 5)


= {(1, 3), (1, 5), (3, 3), (3, 5)}


(iv) Given: A = {-3, -1}


From part (iii), we get B × C = {(1, 3), (1, 5), (3, 3), (3, 5)}


So,


A × (B × C) = {-3, -1} × {(1, 3), (1, 5), (3, 3), (3, 5)}


= (-3, 1, 3), (-3, 1, 5), (-3, 3, 3), (-3, 3, 5), (-1, 1, 3), (-1, 1, 5), (-1, 3, 3), (-1, 3, 5)}


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