Learn about the Law of Detachment In this lesson, let’s learn about the law of detachment when it comes to conjectures and conditional statements. We need to show or determine if the conjectures given to us are valid by the law of detachment. The law of detachment basically says if P then Q is true, if this is indeed true, and if P is true, then Q must also be true. And I used this as the basis for solving these types of problems. So let’s determine if the conjectures are valid by this law. So we need to identify the hypothesis and the conclusion, and if the hypothesis is true, we have to show the Q, which is the conclusion must also be true. So first one says, if the side lengths of a triangle are 4 feet and 3 feet, so the hypothesis is side lengths of a rectangle are 4 feet and 2 feet, conclusion is its area is 8 feet square. So conjecture says the area of the rectangle is 8 feet square, if the statement says the rectangle has side lengths of 4 feet and 2 feet so let’s see. Based on this, does this fit the hypothesis? The rectangle has side lengths of 4 feet and 2 feet, so it does fit. So this is correct. Then the conjecture says, if this is true then the area of rectangle is 8 ft2. Well, that matches the conclusion because the area of this rectangle would be 4 times 2 ft2. So this is a valid conjecture. Let’s use the second example which says, if you want to go on a fieldtrip, you must have a signed slip. So the hypothesis says if you want to go on a fieldtrip, then the conclusion is you must have a signed slip. So the statement says Elizabeth has a signed permission slip so the conclusion is true, but the conjecture says Elizabeth want to go on a fieldtrip. Well that maybe not be valid because she may have a signed fill slip, but she may never have wanted to go on the trip. She may have done it for other reasons. So this particular conjecture is not valid because even though Elizabeth has a fill slip that is signed, so the conclusion is true. We don’t know if it was because she wanted to go on a field trip or not.