EXERCISE 13.4 Q NO. 2, 3 AND 4

(p^^~q) is logically equal to 1. p -> q 2. ~ p->q 3. p -> ~ q 4. ~(p ->q)

Let R = {(1, 2), (2, 2), (1, 1), (4,4), (1,3), (3, 3), (3,2)} be a relation on the set {1,2,3,4}. Then,

Find : (i) 7/3 -: 2 (ii) 4/9 -: 5 (iii) 6/13 -: 7 (iv) (4) 1/3 -: 3 (v) (3)1/2 -: 4 (vi) (4) 3/7 -: 7

Exercise 2. Let R (1, 3), (2, 5), (3, 7), (4, 9), (5, 11) be a relation in the set A ={1, 2, 3, 4 ,5 }Find the domain and range of R

Let A = {1,2,3,4} and f : A to A satisfy f (1) =2, f(2)=3, f(3)=4, f (4)=1. Suppose g:A to A satisfies g (1) =3 and fog = gof , then g = (a).{(1,3), (2,1), (3,2), (4,4)} (b).{(1,3), (2,4),(3,1),(4,2)} (c).{(1,3),(2,2),(3,4),(4,3)} (d).{(1,3),(2,4),(3,2),(4,1)}

Evaluate the following: ([(1,3),( -1,-4))]+[(3 ,-2 ),(-1 ,1)]) [(1 ,3,5),( 2 ,4 ,6)]

Show that + 1/4 + (1.3)/(4.8) + (1.3.5)/(4.8.12) + …….= sqrt2

The common tangent of Parabola y^2=4x and Hyperbola (x^2)/4-(y^2)/3=1 touches them at P and Q respectively, then Q can be (4, 3) (2) (3, 4) (-4,-3) (4) (4,-3)

The mean of 1,7,5,3,4 and 4 is m. The numbers 3,2,4,2,3,3 and p have mean m-1 and median q. Find p and q

Let A={1,2,3,4} and R be a relation in given by R= (1,1), (2, 2), (3. 3). (4,4), (1,2), (2,1),(3,1), (1,3)} . Then R is