Conjunction questions with solutions are given here to practice and understand logical connectives. Conjunction is a logical connective that joins two statements by ‘AND’ logic operation. It is denoted by the symbol ‘∧’.

Let us understand this with an example; consider the following two statements:

P: I will go to the market

Q: I will bring groceries.

Then P ∧ Q: I will go to the market and bring groceries.

Thus, the logical meaning of conjunction is adding two statements together.

The truth table of conjunction is:

Learn more about Conjunction.

Conjunction Questions with Solutions

Question 1:

Spilt each statement into simple statements:

(i) The sun rises from the east and sets in the west.

(ii) x = 5 and x = 2 are the roots of the equation 3x² – x – 10 = 0.

Solution:

(i) p: The sun rises from east

q : The sun sets in the west

(ii) p: x = 5 is the root of the equation 3x² – x – 10 = 0

q: x = 2 is the root of the equation 3x² – x – 10 = 0

Question 2:

Form a compound conjunction statements with the following simple statements:

(i) p: Lucknow is in Uttar Pradesh

q: Dehradun is in Uttarakhand

(ii) p: 2 is a rational number

q: √2 is an irrational number

Solution:

(i) p ⋀ q: Lucknow is in Uttar Pradesh, and Dehradun is in Uttarakhand.

(ii) p ⋀ q: 2 is a rational number, and √2 is an irrational number.

Question 3:

Split each statement into simple statements and determine whether their conjunction is true or false.

(i) 36 is divisible by 2 and 6.

(ii) x = 1 and x = 2 are the roots of the equation x² – x – 2 = 0.

(iii) All integers are rational numbers, and all rational numbers are integers.

Solution:

(i) Let p: 36 is divisible by 2

q: 36 is divisible by 9.

Both p and q are true individually.

∴ (p ⋀ q) = True.

(ii) Let p: x = 1 is the root of the equation x² – x – 2

q: x = 2 is the root of the equation x² – x – 2

q is true but p is false

∴ (p ⋀ q) = False.

(iii) Let p: All integers are rational numbers

q: All rational numbers are integers

p is true, but q is false

∴ (p ⋀ q) = False.

Question 3:

Form a conjunction statement with

p: Ria like roses

q: Ria likes lilies

Solution:

Ria likes roses and lilies.

Also Read:

• Mathematical Logic
• Boolean Algebra
• Truth Tables
• Conditional Statements

Question 4:

Write the truth table for the statement: ~(p ⋀ ~q)

Solution:

Question 5:

Verify using the truth table ~(p ⋀ q) = ~p ⋀ ~q.

Solution:

∴ ~(p ⋀ q) ≠ ~p ⋀ ~q

Question 6:

Let p: It is raining outside, and q: It is cold. Give simple verbal statements for the following statements:

(i) ~p ⋀ q

(ii) p ⋀ ~q

(iii) ~p ⋀ ~q

Solution:

(i) It is not raining outside, and it is cold.

(ii) It is raining outside, and it is not cold.

(iii) It is not raining outside, and it is not cold.

Question 7:

Prove that p ⋀ ~p is a contradiction.

Solution:

∴ p ⋀ ~p is a contradiction.

Also Check:

• Class 11 Mathematical Reasoning Notes
• Class 11 Study Materials

Question 8:

Construct a truth table for the proposition: p ⋀ ~(p ⋀ q).

Solution:

Question 9:

Construct a truth table for the proposition: ~p ⋀ (~p ⋀ q).

Solution:

Question 10:

Prove that the proposition p V ~(p ⋀ q) is a tautology.

Solution:

∴ p V ~(p ⋀ q) is a tautology.

Practice Questions on Logical Conjunction

1. Split each statement into simple statements and determine whether their conjunction is true or false.

(i) A = {x: x + 5 ≤ 10} and 5 ∈ A.

(ii) A ⋂ B = ϕ and x ∈ A, x ∈ B

(iii) Mars is a planet in our solar system and moon is a natural satellite of Earth.

(iv) x = 1 and x = 2 are the roots of the equation 2x + 5 = 7.

2. Construct a truth table for the following propositions:

(i) (A ⋀ ~B) ⋀ (A ⋀ B)

(ii) p ⋀ ~(~q ⋀ p)

(iii) p V (~p ⋀ ~q)

3. Verify the statement: ~(a V b) = ~a ⋀ ~b.

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