For each of the following determine whether the relation on the given set is reflexive, symmetric, transitive, and an equivalence relation (where ⇐⇒ means if and only if). Justify each of your answers (with proof or counterexamples).

1. R={(f, g)|f(1)=g(1)}on the set A={f|f:Z→Z}
2. R={(f, g)|f(0)=g(0)or f(1)=g(1)}on set A={f|f:Z→Z}
3. ((a, b),(c, d))∈R⇐⇒a+d=b+c on A=Z×Z
4. xRy⇐⇒x−y ∈ Z on A=R

The surface area (sa) of a cube with a as the length of each of its sides is given by the formula . if the surface area is known, how can you rewrite the formula to find its side?

Hardest math question of all time can you solve the equation. check for extraneous solutions.9∣9-8x∣ = 2x+3

Barney & noblet customers can choose to purchase a membership for $25 per year members receive 10% off all store purchases 1. how much would a member pay per year if he bought $50 worth of items each year? 2. write a slope-intercept equation that expresses how much a member pays per year using x to represent his purchases per year 3. how much would a member have to spend per year to pay off his membership fee?