Answers:
(i) Direct Method:
Consider,
q: x is a real number such that x3 + x=0.
r: x is 0.
If q, then r.
Let q be true. Then, x is a real number such that x3 + x = 0
x is a real number such that x(x2 + 1) = 0
x = 0
r is true
q is true
q is true and r is true.
Thus, p is true.
(ii) Method of Contrapositive:
Let,
R is not true
x ≠ 0, x∈R
x(x2+1)≠0, x∈R
q is not true
-r = -q
p : q and r is true