If $A = \{1, 2, 3, 4, 5\}$ then which of the following is not true?
- A$Ǝ x \in A$ such that $x + 3 = 8$
- B$Ǝ x \in A$ such that $x + 2 < 9$
- ✓$Ɐ x \in A, x + 6 \geq 9$
- D$Ǝ x \in A$ such that $x + 6 < 10$
Answer: C.
View full solution →Question types
Mathematical Logic question types
374 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
374
Questions
7
Question groups
5
Question types
01
MCQ
148 Q→02Write true or false if statement is wrong write the true statement.
27 Q→03Answer the following questions in short.
84 Q→04Solve the Following Question.(2 Marks)
69 Q→05Solve the Following Question.(3 Marks)
24 Q→06Solve the Following Question.(4 Marks)
5 Q→07Do as instructed
17 Q→Sample Questions
Mathematical Logic questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The negation of p ∧ (q → r) is ________.
- A~p ∧ (~q → ~r)
- Bp ∨ (~q ∨ r)
- C~p ∧ (~q → ~r)
- ✓~p ∨ (~q ∧ ~r)
Answer: D.
View full solution →The negation of inverse of ~p → q is ________.
- ✓q ∧ p
- B~p ∧ ~q
- Cp ∧ q
- D~q → ~p
Answer: A.
View full solution →If p ∧ q is F, p → q is F then the truth values of p and q are ________.
- AT, T
- ✓T, F
- CF, T
- DF, F
Answer: B.
View full solution →Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________.
- A(p ∧ q) → (p ∨ q)
- B~(p ∨ q) → (p ∧ q)
- ✓(~p ∧ ~q) → (~p ∨ ~q)
- D(~p ∨ ~q) → (~p ∧ ~q)
Answer: C.
View full solution →If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of each of the following statement : Ɐ x ∈ A, 3x ≤ 25.
If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of each of the following statement : Ǝ x ∈ A, such that x + 7 ≥ 11.
If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of each of the following statement : Ɐ x ∈ A, x + 5 < 12.
If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of each of the following statement : Ǝ x ∈ A such that x + 8 = 15.
It rains heavily.
Write the truth values of the following statements :
Ɐ n ∈ N, n + 6 > 8.
Write the truth values of the following statements :
In ∆ ABC if all sides are equal then its all angles are equal.
Write the truth values of the following statements :
The square of any even number is odd or the cube of any odd number is odd.
Write the truth values of the following statements :
Ǝ n ∈ N such that n + 5 > 10.
Write the truth values of the following statements :
$\forall n \in N, n^2+n$ is even number while $n ^2- n$ is an odd number.
View full solution →$\forall n \in N, n^2+n$ is even number while $n ^2- n$ is an odd number.
Using truth tables prove the following logical equivalences : (p ∧ q) → r ≡ p → (q → r)
Using truth tables prove the following logical equivalences : p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Using the rules in logic, write the negations of the following : (~p ∧ q) ∨ (p ∧ ~q)
Using the rules in logic, write the negations of the following : (p → q) ∧ r
Using the rules in logic, write the negations of the following : p ∧ (q ∨ r)
Express the following circuits in the symbolic form. Prepare the switching table :
Express the following circuits in the symbolic form. Prepare the switching table :
In the following switching circuit,: Simplify the circuit
In the following switching circuit,: Construct switching table
Simplify the given circuit by writing its logical expression. Also,write your conclusion.
Simplify the following so that the new circuit has minimum number of switches. Also, draw the simplified circuit.
Simplify the following so that the new circuit has minimum number of switches. Also, draw the simplified circuit.
Write the symbolic form of the following switching circuits construct its switching table and interpret it.
Write the symbolic form of the following switching circuits construct its switching table and interpret it.
Write the symbolic form of the following switching circuits construct its switching table and interpret it.
Construct the truth table for each of the following statement patterns.
i) $\quad p \rightarrow(q \rightarrow p)$
ii) $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$
iii) $\sim(\sim p \wedge \sim q) \vee q$
iv) $[(p \wedge q) \vee r ] \wedge[\sim r \vee(p \wedge q)]$
v) $[(\sim p \vee q) \wedge(q \rightarrow r )] \rightarrow(p \rightarrow r )$
View full solution →i) $\quad p \rightarrow(q \rightarrow p)$
ii) $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$
iii) $\sim(\sim p \wedge \sim q) \vee q$
iv) $[(p \wedge q) \vee r ] \wedge[\sim r \vee(p \wedge q)]$
v) $[(\sim p \vee q) \wedge(q \rightarrow r )] \rightarrow(p \rightarrow r )$
Write the negations of the following.
i) Price increases
ii) 0! ≠ 1
iii) 5 + 4 = 9
i) Price increases
ii) 0! ≠ 1
iii) 5 + 4 = 9
If statements p, q are true and r, s are false, determine the truth values of the following. i) i) $\sim p \wedge(q \vee \sim r )$
ii) $(p \wedge \sim r ) \wedge(\sim q \vee s )$
iii) $\sim(p \rightarrow q) \leftrightarrow( r \wedge s )$
iv) $(\sim p \rightarrow q) \wedge( r \leftrightarrow s )$
View full solution →ii) $(p \wedge \sim r ) \wedge(\sim q \vee s )$
iii) $\sim(p \rightarrow q) \leftrightarrow( r \wedge s )$
iv) $(\sim p \rightarrow q) \wedge( r \leftrightarrow s )$
Write the truth values of the following statements.
i) 3 is a prime number and 4 is a rational number.
ii) All flowers are red or all cows are black.
iii) If Mumbai is in Maharashtra then Delhi is the capital of India.
iv) Milk is white if and only if the Sun rises in the West.
i) 3 is a prime number and 4 is a rational number.
ii) All flowers are red or all cows are black.
iii) If Mumbai is in Maharashtra then Delhi is the capital of India.
iv) Milk is white if and only if the Sun rises in the West.
Express the following compound statements symbolically without examining the truth values.
i) 2 is an even number and 25 is a perfect square.
ii) A school is open or there is a holiday.
iii) Delhi is in India but Dhaka is not in Srilanks.
iv) 3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25.
i) 2 is an even number and 25 is a perfect square.
ii) A school is open or there is a holiday.
iii) Delhi is in India but Dhaka is not in Srilanks.
iv) 3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25.
Generate a Mathematical Logic paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.