Sketch the graph of the curve y = sin x + π 2 .

We have y = sin x + π 2 . We know the graph of y = sin x + π 2 is obtained by shifting the graph of y = sin x by π 2 units towards left along the x -axis. Hence, the graph of y = sin x + π 2 is given below

Sketch the graph of the curve y = sin x + π 2 .

We have y = sin x + π 2 . We know the graph of y = sin x + π 2 is obtained by shifting the graph of y = sin x by π 2 units towards left along the x -axis. Hence, the graph of y = sin x + π 2 is given below

If A = 1 , 3 , 5 , 9 and B = 2 , 11 , find A × B .

Given that A = 1 , 3 , 5 , 9 and B = 2 , 11 . We know that, the cross product A × B = a , b , a ∈ A , b ∈ B . ∴ A × B = 1 , 2 , 1 , 11 , 3 , 2 , 3 , 11 , 5 , 2 , 5 , 11 , 9 , 2 , 9 , 11 .

If A × B = a , 1 , b , 3 , a , 3 , b , 1 , a , 2 , b , 2 . Find A and B .

We know that, the cross product of two sets is defined as A × B = x , y , x ∈ A , y ∈ B . Also, if n A = p and n B = q then n A × B = p q , where n A denotes the number of elements in the set A . Given that A × B = a , 1 , b , 3 , a , 3 , b , 1 , a , 2 , b , 2 . Hence A = set of first elements in A × B i.e. A = a , b . And B = set of second elements in A × B i.e. B = 1 , 2 , 3 .

Let A and B be two sets such that A × B consists of 6 elements. If three elements of A × B are 1 , 4 , 2 , 6 , 3 , 6 . Find A .

We know that, the cross product A × B = x , y , x ∈ A , y ∈ B . Also, if n A = p and n B = q then n A × B = p q , where n A denotes the number of elements in the set A . Given three elements of A × B are 1 , 4 , 2 , 6 , 3 , 6 . Hence, the first element belongs to the set A and the second element belongs to the set B . So, we can say that A = 1 , 2 , 3 and B = 4 , 6 .

If P = a , b , c , find P × P .

We know that, the cross product of two sets is defined as A × B = x , y , x ∈ A , y ∈ B . Also if n A = p and n B = q then n A × B = p q , where n A denotes the number of elements in the set A . Given P = a , b , c . ∴ P × P = a , a , a , b , a , c , b , a , b , b , b , c , c , a , c , b , c , c .

Let A = 2 , 3 and B = 5 , 6 . Write A × B . How many subsets will A × B have?

We know that, the cartesian product of two non-empty sets X and Y is defined as X × Y = x , y : x ∈ X , y ∈ Y . Given A = 2 , 3 and B = 5 , 6 . Hence A × B = 2 , 4 , 2 , 5 , 3 , 4 , 3 , 5 . Thus, the number of elements in A × B is 4 . We also know that a set with n elements will have 2 n subsets. Since, n A × B = 4 , hence A × B will have 2 4 = 16 subsets.