Let `T={x: (x+5)/(x-7)-5=(4x-40)/(13-x)}`.Is T an emply set?
Justify your answer.

Let A = R - {-3} and B = R - {1} Consider the function f : A rarr B defined by f(x) = (x-2)/(x-3) . Is f one-one and onto ? Justify your answer.

Let A=R-{3} and B=R-{1} consider the function f:AtoB defined by f(x)=frac(x-2)(x-3) . Is f one-one and onto? Justify your answer.

Let A=R-{3} and B=R-{1} Consider the function f:ArarrB defined by f(x)=frac(x-2)(x-3) Is f one-one and onto? Justify your answer.

Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions defined by f(x)=x^2-x, x in A and g(x)=2|x-1/2|-1, x in A .Are f and g equal?. Justify your answer.

Consider f:RtoR given by f(x)=5x+2 Is f invertible? Justify your answer.

Let ast be an operation such that aastb=LCM of a and b defined on the set A={1,2,3,4,5} . Is ast a binary operation? Justify your answer.

Given a non empty set X , consider P(X) which is the set of all subsets of X . Define the relation R in P(X) as follows. For subsets A, B in P(X) , A R B if and only of A sub B . Is R an equivalence relation on P(X) . Justify your answer.

Let R be a Relation in the set A={1,2,3,4,5,6} define as R={(x,y):y=2x-1} Is R an equivalance relation? Justify.

Solve x/2 lt (5x-2)/3 - (7x-3)/5 and draw the graph of the solution set.