Prove the following statements Hint: Use Contrapositive and DeMorgan's laws to reduce each line to the statements in problem II. Use A for ∀,"For all" and E for ∃,"There exists" a.) ∃xC(x) + ∃xB(x) <=> ∃x[C(x) + B(x)] show <=> to ∀xP(x)* ∀xQ(x)<=> ∀x [P(x) * Q(x)]

Describe the symmetry of the figure. identify lines of symmetry, if any. find the angle and the order of any rotational symmetry.

Evaluate the expression for the given value of the variable. 5×(h+3) for h=7

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.