If `A={1,\ 2,\ 3,\ 4}` and `B={a ,\ b ,\ c ,\ d}` . Define any four bijectives from `A` to `B` . Also, give their inverse functions.

If f: Rvec is defined by f(x)=2x+7. Prove that f is a bijection. Also, find the inverse of fdot

If f:R-R is defined by f(x)=2x+7. Prove that f is a bijection. Also, find the inverse of f .

If A={1,2,3) and B={a,b} , then the number of functions from A to B is

If A={a,b,c} and B={-3,-1,0,1,3} , then the number of injections that can be defined from A to B is .

Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ d) a+d=b+c for all (a ,\ b),\ (c ,\ d) in NxxN is an equivalence relation. Also, find the equivalence classes [(2, 3)] and [(1, 3)].

The total no of bijective functions from set {x,y,z} to set {a,b,c} is

If A={1,2,3},\ B={x , y} , then the number of functions that can be defined from A into B is 12 b. 8 c. 6 d. 3

Let A={x in R :-1lt=xlt=1}=B and C={x in R : xgeq0} and let S={(x ,\ y) in AxxB : x^2+y^2=1} and S_0={(x ,\ y) in AxxC : x^2+y^2=1}dot Then S defines a function from A to B (b) S_0 defines a function from A to C (c) S_0 defines a function from A to B (d) S defines a function from A to C

Let A={a ,\ b ,\ c} , B={u\ v ,\ w} and let f and g be two functions from A to B and from B to A respectively defined as: f={(a ,\ v), (b ,\ u),\ (c ,\ w)} , g={(u ,\ b),\ (v ,\ a),\ (w ,\ c)}dot Show that f and g both are bijections and find fog and gofdot

Consider set A = {x_(1), x_(2), x_(3), x_(4), x_(5)} and set B = {y_(1), y_(2), y_(3)} . Function f is defined from A to B. Number of function from A to B such that f(x_(1)) = y_(1) and f(x_(2)) != y_(2) is