1
GATE CSE 2002
MCQ (Single Correct Answer)
+1
-0.3
"If X then Y unless Z" is represented by which of the following formulas in propositional logic? (" $$\neg $$ " is negation, " $$ \wedge $$ " is conjunction, and " $$ \to $$ " is implication)
A
$$\left( {{\rm X} \wedge \neg Z} \right) \to Y$$
B
$$\left( {X \wedge Y} \right) \to \neg Z$$
C
$${\rm X} \to \left( {Y \wedge \neg Z} \right)$$
D
$$\left( {{\rm X} \to Y} \right) \wedge \neg Z$$
2
GATE CSE 2002
MCQ (Single Correct Answer)
+2
-0.6
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is
A
1/16
B
1/8
C
7/8
D
15/16
3
GATE CSE 2002
MCQ (Single Correct Answer)
+2
-0.6
The binary relation $$S = \phi $$ (emply set) on set A = {1, 2, 3} is
A
Neither reflexive nor symmetric
B
Symmetric and reflexive
C
Transitive and reflexive
D
Transitive and symmetric
4
GATE CSE 2002
Subjective
+5
-0
Determine whether each of the following is a tautology, a contradiction, or neither ("$$ \vee $$" is disjunction, "$$ \wedge $$" is conjuction, "$$ \to $$" is implication, "$$\neg $$" is negation, and "$$ \leftrightarrow $$" is biconditional (if and only if).

(i)$$\,\,\,\,\,\,A \leftrightarrow \left( {A \vee A} \right)$$
(ii)$$\,\,\,\,\,\,\left( {A \vee B} \right) \to B$$
(iii)$$\,\,\,\,\,\,A \vee \left( {\neg \left( {A \vee B} \right)} \right)$$

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