12TH MATHS| CHAPTER 01 MATHEMATICAL LOGIC PYQS

CHAPTER 01: MATHEMATICAL LOGIC

One Mark Questions

1. Write the dual of p ∧ ¬p = F

February 2020

Solution:
The dual is obtained by interchanging ∧ with ∨ and T with F.
Dual: p ∨ ¬p = T

Answer: p ∨ ¬p = T

2. If p, q are true and r, s false, find truth value of (p → q) ∨ (r → s)

July 2020

Solution:
p→q = T→T = T
r→s = F→F = T
T ∨ T = T
Answer: T

Two Marks Questions

1. Write in symbolic form:

March 2023

a) A triangle is equilateral iff it is equiangular
Symbolic form: p ↔ q

b) Price increases and demand falls
Symbolic form: p ∧ q

2. For A = {2,3,4,5,6}, which is not true?

October 2013

1. ∃x∈A: x+3=8 (True: x=5)
2. ∃x∈A: x+2<5 (True: x=2)
3. ∃x∈A: x+2<9 (True for all elements)
4. ∀x∈A: x+6≥9 (False: x=2 gives 8)

Answer: (d)

3. Write the dual of:

March 2014

a) (p ∨ q) ∧ T
Dual: (p ∧ q) ∨ F

b) Madhuri has curly hair and brown eyes
Dual: Madhuri has curly hair or brown eyes

4. Write truth values:

October 2014

a) √5 is irrational but 3 is rational
Truth value: T ∧ T = T

b) ∃n∈N: n+5>10
Truth value: True (n=6 satisfies)
Answer: T

5. Write converse and contrapositive of:

March 2015

"If two triangles are congruent then their areas are equal"
Converse: "If areas are equal, then triangles are congruent"
Contrapositive: "If areas are unequal, then triangles are not congruent"

6. If p∧q=F and p→q=F, find truth values

October 2015

Solution:
p→q=F only when p=T and q=F
Then p∧q = T∧F = F (matches given condition)
Answer: (b) T, F

7. Negation of p∧(q→r) is:

March 2016

Solution:
¬(p∧(q→r)) ≡ ¬p∨¬(q→r)
≡ ¬p∨(q∧¬r)
Answer: (d)

8. Inverse of (p∨q)→(p∧q)

July 2016

Solution:
Inverse: ¬(p∨q)→¬(p∧q)
≡ (¬p∧¬q)→(¬p∨¬q)
Answer: (d)

9. Find truth value of (r∧q)↔¬p when p=T, q=F, r=T

July 2016

Solution:
r∧q = T∧F = F
¬p = ¬T = F
F↔F = T
Answer: T

10. [Statement Missing]

March 2017

Note: Original statement not available in question paper