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in Mathematical Reasoning by (15.2k points)

For each of the following compound statement first identify the connecting words and then break it into component statement:

1. All rational numbers are real and all real numbers are not complex.

2. Square of an integer is positive or negative.

3. The sand heats up quickly in the sun and does not cool down fast at night.

x = 2 and x = 3 are the roots of the equation 3x2 – x – 10 = 0

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1 Answer

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by (15.7k points)

1. The component statement has the connecting word ‘and’ component statements are

p: All rational numbers are real

q: All real numbers are not complex.

2. The component statement has the connecting word ‘or’ component statements are

p: Square of an integer is positive.

q: Square of an integer is negative.

3. The component statement has the connecting word ‘and’ component statements are

p: The sand heats up quickly in the sun.

q: The sand does not cool down fast at night.

4. The component statement has the connecting word ‘and’ component statements are

p: x = 2 are the roots of the

equation 3x2 – x – 10 = 0.

q: x = 3 are the roots of the equation 3x2 – x – 10 = 0.

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