**Q1: **

Consider the following two statements.

Statement 1: If A is true, then B is true.

Statement 2: A is true.

If both statements are true,
then the law of detachment allows us to conclude that B is true.

Statement 1: If and are odd numbers,
then is odd.

Statement 2: and are odd numbers.

What can we conclude about ?

Statement 3: If is an odd number,
then is prime.

Statement 4: is an odd number.

Can we conclude is prime? Why?

**Q2: **

Consider the following two statements:

Statement 1: If A is true, then B is true.

Statement 2: If B is true, then C is true.

If both statements are true, then the law of syllogism tells us that we can write a third true statement:

Statement 3: If A is true, then C is true.

Given statements 3 and 4 below, which of the following statements is also true?

Statement 3: If is odd, then both and are odd.

Statement 4: If both and are odd, then is even.

Statement 5: If a shape is a square, then it has a right angle.

Statement 6: If a shape is a square, then it has a pair of parallel sides.

Shape has a right angle and a pair of parallel sides. What can we conclude about shape from the given statements?