Students can Download Basic Maths Exercise 6.1 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka 2nd PUC Basic Maths Question Bank Chapter 6 Mathematical Logic Ex 6.1

Part – A

**2nd PUC Basic Maths Mathematical Logic Ex 6.1 One Mark Questions and Answers**

Question 1.

Symbolise the following propositions:

(1) 3x = 9 and x<7

(ii) 33 + 11 ≠ 3 or 8 – 6 = 2

(iii) If two numbers and equal then their squares are not equal.

(iv) If oxygen is a gas then gold is a compound

(v) y + 4 ≠ 4 ore is not a vowel

Answer:

(i) Let p:3x = 9, q = x < 7

Given in symbols is p ∧ q

(ii) Let p:33 = 11 = 3, q= 8 – 6 = 2

Given is ~p ∨ q

(iii) Let p: Two numbers are equal, q: Squares are equal then given is p → ~q

(iv) Let p: Oxygen is a gas

q: Gold is a compound

Then given is p → q

(v) P: y + 4 = 4, q: e is a vowel given proposition is ~p v ~q

Part – B

**2nd PUC Basic Maths Mathematical Logic Ex 6.1 Two or Three Marks Questions and Answers**

Question 1.

if p, q and r are propositions with truth values F, T and F respectively, then find the truth values of the following compound propositions:

(i) (~p → q) ∨ r

(ii) (p ∧ ~q) → r

(iii) p → (q → r)

(iv) ~(p → q) ∨~(p ↔ q)

(v) (p ∧ q) ∨ ~ r

(vi) ~(p ∨ r) → ~q

Answers:

(i) (~p → q)∨ r

(~F →T) ∨ r

(T →T) ∨ F

T ∨ F

= T

(ii) (p ∧~q) → r

(F∧ ~T) → F

(F ∧F) → F

F →F

= T

(iii) p → (q → r)

F →(T →F)

F →(T →F)

= T

(iv) ~(p → q) ∨~(p↔ q)

~(F →T) ∨ ~(F↔T)

~T ∨ ~F

F ∨ T = T

(v) (p ∧ q) ∨ ~ r

(F ∧ T) ∨ ~ r

F ∨ T

= T

(vi) ~(P ∨ r) → ~ q

~(F ∨ F) ∨ ~ T

~F → ~ T

T → F

= F

Question 2.

Answer:

(1) If the compound proposition “(p → q) ∧ (p ∧ r)” is false, then find the truth values of p, q and r.

(ii) If the compound proposition p→ (q ∨ r) is false, then find the truth values of p, q and r.

(iii) If the compound proposition p → (~q ∨ r) is false, then find the truth values of p, q and r.

(iv) If the truth value of the propositions (p ∧ q) → (r ∨ ~s) is false, then find the truth values of p, q, rand s.

Answers:

(i) Given (p → q) ∧ (p ∧ r) is false

(a) Case 1: p → q is true & p ∧ r is false

p is T q is T & p is T &ris F

p = T, q = T, r = F

Case 2(a): p = F, q = T p ∧ r= F → p = F, r = F

p = F, q = T, r = f

(b): (p →q) is F & par is true

T → F = F

T ∧ T is T

P=T, q = F, r=T

Case 3: (p → q) is F & (p ∧ r) is false

T → F = F

F ∧ F = F

F ∧ T = F

F ∧ F = F .

∴ p = T, q = F, r= F.

(ii) Given p → (q ∨ r) is false

T → F = F

∴ p = T & q ∨ r is false =

F ∨ F= F

∴ p = T, q = F & r= F

(iii) Given p → (q ∨ r) is false

Then T → F= F

∴ P = T, ~ q ∨ r= F

F ∨ F = F

∴ q = T, q = T, r = F.

(iv) Given (p ^ q) → (r ∨ ~s) is false

We know that T → F = F

∴ p∧q = T and r ∨ ~s = F is false

T∧ T = T

F ∨ F= F is false

∴ p = T, q = T, r = F, S = T