Show geometrically that the set S=`{(x,y):x^(2)+y^(2)lt4}` is a convex set

Find the area of the region { (x,y): x^(2)lt y lt |x| }

The value of 'c' for which the set {(x, y)|x^2+y^2+2xle1}bigcap{(x, y)|x-y+cge0)} contains only one point in common is

A relation S is defined on the set of real numbers R R a follows : S{(x,y) : x^(2) +y^(2)=1 for all x,y in R R } Check the relation S for (i) reflexivity (ii) symmetry an (iii) transitivity.

If A={1,2,3,4,5}, show that the relation f={(x,y):x+y=6} for all x,y in A , defines a mapping from A to itself, but the relation g= {(x,y):y lt x} does not defines a mapping in set A.

Find the area of the region {(x , y): y^2lt=4x ,4x^2+4y^2lt=9}

The area of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^2 lt= 1- x} is

If A = {1, 2, 3, 4, 5, 6}, show that the relation f={(x,y):x+y=7}, for all x,y in A defines a mapping from A to itself but the relation g={(x,y):x+y gt8} does not define a mapping in set A.

Find the feasible region if any graphically for the case : x+2y lt4 x+2ygt6 and xgt0, y gt 0

The solution set of the inequlity (|x-2|-x)/(x)lt2 is