1
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
Consider two well-formed formulas in propositional logic
$$F1:P \Rightarrow \neg P$$
$$F2:\left( {P \Rightarrow \neg P} \right) \vee \left( {\neg P \Rightarrow } \right)$$

Which of the following statements is correct?

A
F1 is satisfiable, F2 is valid
B
F1 is unsatisfiable, F2 is satisfiable
C
F1 is unsatisfiable, F2 is valid
D
F1 and F2 are both satisfiable
2
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day ?
A
$$1/{7^7}$$
B
$$1/{7^6}$$
C
$$1/{2^7}$$
D
$$7/{2^7}$$
3
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Let $$f:\,A\, \to B$$ be a function, and let E and F be subsets of A. Consider the following statements about images.

$$S1:\,f\,\left( {E\, \cup \,F} \right)\, = \,f\left( E \right)\, \cup \,f\,\left( F \right)$$
$$S2:\,f\,\left( {E\, \cap \,F} \right)\, = \,f\left( E \right)\, \cap \,f\,\left( F \right)$$
Which of the following is true about S1 and S2?

A
Only S1 is correct
B
Only S2 is correct
C
Both S2 and S2 are correct
D
None of S1 and S2 is correct
4
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Consider the following statements:

S1: There exist infinite sets A, B, C such that
$$A\, \cap \left( {B\, \cup \,C} \right)$$ is finite.
S2: There exist two irrational numbers x and y such that (x + y) is rational.
Which of the following is true about S1 and S2?

A
Only S1 is correct
B
Only S2 is correct
C
Both S1 and S2 are correct
D
None of S1 and S2 is correct
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