Give an example of vectors and such that but

Let A= {1,2,3,4}. Let R be the equivalence relation on A × A defined by (a,b)R(c,d) iff a + d = b + c . Find the equivalence class [(1,3)].

If ij A [a_ij] is a matrix of order 2 × 2, such that |A|= -15 and C_ij represents the cofactor of , a_ij a then find a₂₁ c₂₁ + a₂₂ c₂₂.

Determine whether the binary operation * on the set N of natural numbers defined by a*b = 2^ab is associative or not.

If 4sin^-1x + cos^-1x = π, then find the value of x.