Check validity: (4) `EE` x `in` N such that x + 6 < 4

Check validity: (2) AA x in R, |x| = x

Find the truth values of the followings: (i) EE x in R such that x ^3 = 1

Show that the following pair of sets are equal A = {x :x is an integer such that .5 < x < 7.5} , B = {1, 2, 3, 4, 5, 6, 7}

Integrate the function int (4 cos x-3 sin x)/((8 sin x + 6 cos x)^(2))dx.

x and y are two positive integers such that 2,x, y are in A.P. and x, y, 9 are in G.P. then show that -x= 4, y= 6.

If x in N ,solve 4x + 5 < 2x + 17

Find a relation between x and y such that the point(x,y) is equidistant from the point (3,6) and (-3,4).

Find the value of a and b so that 6x^4+8x^3-5x2+ax+b is divisible by 2x^2-5 .