Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 1 Mathematical Logic Exercise 1.2 [Page 6]
EXERCISE 1.2Q 1.1 PAGE 6
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
SOLUTION
Let p : e is a vowel.
q : 2 + 3 = 5
The symbolic form is p ∨ q.
EXERCISE 1.2Q 1.2 PAGE 6
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
SOLUTION
Let p : Mango is a fruit.
q : Potato is a vegetable.
The symbolic form is p Λ q.
EXERCISE 1.2Q 1.3 PAGE 6
Express the following statement in symbolic form.
Milk is white or grass is green.
SOLUTION
Let p : Milk is white.
q : Grass is green.
The symbolic form is p ∨ q.
EXERCISE 1.2Q 1.4 PAGE 6
Express the following statement in symbolic form.
I like playing but not singing.
SOLUTION
Let p : I like playing.
q : I do not like singing.
The symbolic form is p ∧ q.
EXERCISE 1.2Q 1.5 PAGE 6
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
SOLUTION
Let p : It is cloudy.
q : It is still raining.
The symbolic form is p ∧ q.
EXERCISE 1.2Q 2.1 PAGE 6
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
SOLUTION
Let p : Earth is a planet.
q : Moon is a star.
The truth values of p and q are T and F respectively.
The given statement in symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ F ≡ F
∴ Truth value of the given statement is F.
EXERCISE 1.2Q 2.2 PAGE 6
Write the truth value of the following statement.
16 is an even number and 8 is a perfect square.
SOLUTION
Let p : 16 is an even number.
q : 8 is a perfect square.
The truth values of p and q are T and F respectively.
The given statement in symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ F ≡ F
∴ Truth value of the given statement is F.
EXERCISE 1.2Q 2.3 PAGE 6
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
SOLUTION
Let p : A quadratic equation has two distinct roots.
q : 6 has three prime factors.
The truth values of p and q are F and F respectively.
The given statement in symbolic form is p ∨ q.
∴ p ∨ q ≡ F ∨ F ≡ F
∴ Truth value of the given statement is F.
EXERCISE 1.2Q 2.4 PAGE 6
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
SOLUTION
Let p : Himalayas are the highest mountains.
q : Himalayas are the part of India in the north east.
The truth values of p and q are T and T respectively.
The given statement in symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ T ≡ T
∴ Truth value of the given statement is T.
