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in Mathematical Reasoning by (15.2k points)

Find the component statements of the following compound statements and check they are true or false.

1. Number 3 is prime or it is odd.

2. All integers are positive or negative.

3. 100 is divisible by 3,11 and 5.

4. The sun shines or it rains.

India is a democracy and a monarchy.

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1 Answer

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by (15.7k points)

1. The component statements are

p: Number 3 is prime

q: Number 3 is odd.

Both the component statements p and q are true.

2. The component statements are

p: All integers are positive

q: All integers are negative.

Both the component statements p and q are true.

3. The component statements are

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

The component statements p and q are false, whereas r is true.

4. The component statements are

p: The sun shines

q: It rains.

Both the component statements p and q are true.

5. The component statements are

p: India is a democracy.

q: India is a monarchy.

Both the component statements p is true, whereas the component statement q is false.

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