3 Marks Question

Question 13 Marks

Write the component statements of the following compound statements and check whether the compound statement is true or false.
2 is an even number and a prime number.

Answer

It is true statements and its component statements are:
p: 2 is an even number. (True).
q: 2 is a prime number. (True).

View full question & answer→

Question 23 Marks

Write the component statements of the following compound statements and check whether the compound statement is true or false.
24 is a multiple of 4 and 6.

Answer

Here, the given statement is of the form p $\land \,$ q which has the truth value T whenever both p and q have the truth value T. Hence, it is a true statement and its component statement are:
p: 24 is a multiple of 4. (True).
q: 24 is a multiple 6. (True).

View full question & answer→

Question 33 Marks

Check the validity of the following statement.
p : 125 is divisible by 5 and 7.

Answer

Given that:
p: 125 is divisible by 5 and 7.
Let q: 125 is divisible by 5.
and r: 125 is divisible by 7.
Here q is true and r is false.
⇒ $\text{q}\land \text{r}$ is false.
Here, p is not valid.

View full question & answer→

Question 43 Marks

Prove the following statement by contradication method.
p: The sum of an irrational number and a rational number is irrational.

Answer

Let p be false i.e., sum of an irational and a rational number is rational.
Let $\sqrt{\text{m}}$ is irational and a rational number.
$\Rightarrow \sqrt{\text{m}}+\text{n}=\text{r}$ [rational]
$\Rightarrow \sqrt{\text{m}}=\text{r}-\text{n}$
Now, $\sqrt{\text{m}}$ is irrational, whereas (r - n) is rational.
This is contradiction.
Then, our suppposition is wrong.
Hence, p is true.

View full question & answer→

Question 53 Marks

Write the component statements of the following compound statements and check whether the compound statement is true or false.
All living things have two eyes and two legs.

Answer

It is a false statement. Since. p $\land \,$ q has truth value F whenever either p or q or both have the truth value F. Its component statements are
p: All living things have two eyes. (False).
q: All living things have two legs. (False).

View full question & answer→

Question 63 Marks

Check the validity of the following statement.
q : 131 is a multiple of 3 or 11.

Answer

Given that:
q: 131 is a multiple of 3 and 11.
Let p: 131 is a multiple of 3 .
and r: 131 is is a multiple of 11 .
Here p is not true and r is also not true i.e., false.
So, $\text{q}\lor\text{r}$ is false.
Here, q is not valid.

View full question & answer→

MATHS 3 Marks Question

Test yourself on this topic