Question

if p={1,2,3,4,5}and m ={1,2,4} then p Q=?

Answer 1

Answer:

Given, p,q∈{1,2,3,4}.

For px

2

+qx+1=0 to have real roots,

D=b

2

−4ac≥0

or D=q

2

−4p≥0

q=2⇒p=1

q=3⇒p=1,2

q=4⇒p=1,2,3,4

Hence, 7 values of (p,q).

7 equations are possible.

Answer 2

Step-by-step explanation:

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) }