Answer: The given logical equivalence is proved below.
Step-by-step explanation: We are given to use truth tables to show the following logical equivalence :
P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P)
We know that
two compound propositions are said to be logically equivalent if they have same corresponding truth values in the truth table.
The truth table is as follows :
P Q ∼P ∼Q P⇔ Q ∼P ∨ Q ∼Q ∨ P (∼P ∨ Q)∧(∼Q ∨ P)
T T F F T T T T
T F F T F F T F
F T T F F T F F
F F T T T T T T
Since the corresponding truth vales for P ⇔ Q and (∼P ∨ Q)∧(∼Q ∨ P) are same, so the given propositions are logically equivalent.
Thus, P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P).
Let's define both terms first. Inductive reasoning is a conclusion that you get out of a series of observation. However, this may be true or not. But for deductive reasoning, you reach a conclusion that you get out of a series of observations that are also supported by facts. These are all true.
Since all the statements are based on facts, this is a deductive reasoning.
The answer is B. deductive.
Answer:
<em>Since one of the angles is 90°, the triangle is right.</em>
Step-by-step explanation:
<u>Angles in a Triangle</u>
The sum of angles in a triangle is 180°. We are given the angles are x, 5x, and 6x, thus:
x + 5x + 6x = 180
Simplifying:
12x = 180
Dividing by 12:
x = 180/12 = 15
x = 15°
5x = 75°
6x = 90°
Since one of the angles is 90°, the triangle is right.
Answer:
3 inches to the right
Step-by-step explanation:
The first birdhouse is 27.7 inches to the right
The second birdhouse is 24.9 inches to the left or -24.9 ( left is negative)
The distance between is found by adding the distances
27.7 - (24.9)
27.7-24.9 =2.8
2.8
Rounding to the nearest integer
3 inches apart
Using integers
28 - (25)
3 inches
