Mathematical Logic and Boolean Algebra Test

Result

Mathematical Logic and Boolean Algebra Test - 10

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Question 1
4 / -1

If p, q, r are simple propositions, then (p ˄q) ˄(q ˄r) is true then

A
p, q, r are all false

B
p, q, r are all true

C
p, q are true and r is false

D
p is true and q and r are false

Solution
Question 2
4 / -1

~(p⇒ q) ⇔~ p ˅~ q is

A
A tautology

B
A contradiction

C
Neither a tautology nor a contradiction

D
Cannot come to any conclusion

Solution
Question 3
4 / -1

(p ˄~q) ˄ ( ~p ˅ q) is

A
A contradiction

B
A tautology

C
Either (a) or (b)

D
Neither (a) nor (b)

Solution
Question 4
4 / -1

Which of the following is not logically equivalent to the proposition: \"A real number is either rational or irrational\"?

A
If a number is neither rational nor irrational then it is not real

B
If a number is not a rational or not an irrational, then it is not real

C
If a number is not real, then it is neither rational nor irrational

D
If a number is real, then it is rational or irrational

Solution
Question 5
4 / -1

If p : It rains today, q : I go to school, r : I shall meet any friends and s : I shall go for a movie, then which of the following is the proposition?
If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie,

A
~(p ˄ q) ⇒ (r ˄s)

B
~(p ˄~q) ⇒ (r ˄S)

C
~(p ˄q) ⇒ (r ˅ s)

D
None of these

Solution
Question 6
4 / -1

The negation of the compound proposition p ˅ (~ p ˅ q) is

A
(p ˄~q) ˄~p

B
(p ˄~q) ˅~ p

C
(p ˅~ q) ˅~ p

D
None of these

Solution
Question 7
4 / -1

Which of the following is true?

A
p ⇒q ≡ ~p ⇒ ~q

B
~(p ⇒~q)≡~p˄q

C
~ (~p⇒ ~q)≡ ~p˄q

D
~(p ⇔ q) ≡ [ ~ (p⇒ q)˄~ (q⇒ p)]

Solution
Question 8
4 / -1

~(p ˅ q) ˅ (~ p ˄q) is logically equivalent to

A
~p

B
p

C
q

D
~q

Solution
Question 9
4 / -1

The inverse of the proposition (p ˄ ~q) ⇒ r is

A
~r⇒ ~p˅q

B
~p˅q⇒ ~r

C
r⇒ p˄ ~q

D
None of these

Solution
Question 10
4 / -1

When does the current flow through the following circuit

A
p, q, r should be closed

B
p, q, r should be open

C
Always

D
None of these