Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 1 Mathematical Logic Exercise 1.2 [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 \(p \lor q\).
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 \(p \land q\).
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 \(p \lor q\).
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. (Or: I like singing, then form is \(p \land \neg q\). The original solution implies q is "I do not like singing" directly)
The symbolic form is \(p \land q\).
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 \(p \land q\).
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 \(p \land q\).
\(\therefore p \land q \equiv T \land F \equiv F\)
\(\therefore\) Truth value of the given statement is F.
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 \(p \land q\).
\(\therefore p \land q \equiv T \land F \equiv F\)
\(\therefore\) Truth value of the given statement is F.
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. (Note: A quadratic equation *can* have two distinct roots, but doesn't always. This statement implies it *always* does, which is false. Prime factors of 6 are 2 and 3, so only two prime factors.)
The given statement in symbolic form is \(p \lor q\).
\(\therefore p \lor q \equiv F \lor F \equiv F\)
\(\therefore\) Truth value of the given statement is F.
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 \(p \land q\).
\(\therefore p \land q \equiv T \land T \equiv T\)
\(\therefore\) Truth value of the given statement is T.
