Question

Consider the following two statements.
P : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that f is continuous at x = 1 and g is discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Q : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that both f and g are discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Which one of the following holds ?

• A. Both P and Q are true
• B. Both P and Q are false
• C. P is true but Q is false
• D. P is false but Q is true

Answer 1

Answer: (A)

Both P and Q are true

Answer 2

The correct option is (A) : Both P and Q are true.