GATE 1997
June 3, 2024Question 8815 – Engineering-Mathematics
June 3, 2024Propositional-Logic
| Question 5 |
What is the correct translation of the following statement into mathematical logic?
“Some real numbers are rational”
| ∃x (real(x) ∨ rational(x)) | |
| ∀x (real(x) → rational(x)) | |
| ∃x (real(x) ∧ rational(x)) | |
| ∃x (rational(x) → real(x)) |
Question 5 Explanation:
∃x (real(x) ∧ rational(x))
(A) ∃x(real(x) ∨ rational(x))
means There exists some number, which are either real or rational.
(B) ∀x (real(x)→rational(x))
If a number is real then it is rational.
(D) ∃x (rational(x)→real(x))
There exists a number such that if it is rational then it is real.
Correct Answer: C
Question 5 Explanation:
∃x (real(x) ∧ rational(x))
(A) ∃x(real(x) ∨ rational(x))
means There exists some number, which are either real or rational.
(B) ∀x (real(x)→rational(x))
If a number is real then it is rational.
(D) ∃x (rational(x)→real(x))
There exists a number such that if it is rational then it is real.