Answer:
r=1.8
Step-by-step explanation:
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 F F T F
T F F T T T T T
F T T F T T T T
F F T T F T F F
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).
Answer: The triangles are not congruent.
Step-by-step explanation:
We are given that the two triangles both contain a congruent angle and a congruent side. Additionally, the two triangles also share a side with each other, which is the center horizontal side (the one bisecting the two congruent angles). This "shared" side tells us that this side is congruent in both triangles, meaning that both triangles have two congruent sides with a non-included congruent angle among them.
However, because the two triangles only have two congruent sides, and the angle shared by each triangle is not included between the two sides, the triangle would be "congruent" by SSA, which is not a triangle congruency theorem or postulate.
Therefore, the two triangles are not congruent.
I hope this helps!
Exterior and interior angles added together equal 180 degrees
180-24=156
the answer is 156 degrees
