Question

If P = { 1, 2, 3 } and Q = { 4, 5 } then find P x Q​

Answer 1

The Cartesian product X × Y of sets X , Y is the set of all ordered pairs ( x , y ).

Two ordered pairs ( x1 , y1 ), ( x2 , y2 ) .

Given that P = { 1, 2, 3 } and Q = { 4 , 5 } then,

P x Q = { 1, 2, 3 } x { 4 , 5 }

⇒ P x Q = { 1 } x { 4 , 5 } , { 2 } x { 4 , 5 } , { 3 } x { 4 , 5 }

⇒ P x Q = { 1 , 4 } , { 1 , 5 } , { 2 , 4 } , { 2 , 5 } , { 3 , 4 }, { 3 , 5 }

⇒ P x Q = { (1 , 4 ) , ( 1 , 5 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 3 , 4 ), ( 3 , 5) }