: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r) ⊕ (¬p ∧ q) are logically equivalent.
1 answer:
Answer:
Explanation:
The statements are logically equivalent if they have the same truth tables. So let´s use truth tables in order to determine if they are logically equivalent or not:
The picture that I attached you shows the truth table for each case. As you can see in the highlight columns:
They are logically equivalent because they have exactly the same truth values between each other. Hence, we can conclude that they are logically equivalent.
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Answer:
Yes, the side lengths of 1.5, 2.5, and 2 ft form a right triangle.
Explanation:
Before we solve this problem, we need to know a couple of things.
In a right triangle, you have two legs and a diagonal line that goes from one leg to the other or from one side to the other. This line is called the hypotenuse. It is the longest side of a right triangle. This length can be calculated by using a special formula that is over a thousand years old.
The formula is called the Pythagorean Theorem.
The formula states that if you square one leg and the other leg and add it up. You get the side of hypotenuse which is squared as well.
Here it is in simple terms: .
a and b are your two legs.
C is your hypotenuse.
In this case 1.5 and 2 are your legs and 2.5 is your hypotenuse since it is the longest side.
Before we calculate, there is a converse to the Pythagorean Theorem.
If , then it is not a right triangle.
Lets make 1.5 for a
and 2 for b.
We know 2.5 is for c.
Here it is.
. The / means it is a fraction.
1.5 squared is 9/4 and 2 squared is 4. Add 4 and 9/4 and you get 25/4 squared. Take the square root of 25/4 and you get 5/2.
5/2 is equal to 2.5, so the Pythagorean Theorem applies to this triangle. Therefore, these side lengths do form a right triangle.
Hope this helps!