Recall that a ⇒ b ≡ ¬a ∨ b.
• r ⇒ (p ∧ q) ≡ ¬r ∨ (p ∧ q)
In row C, q is false so p ∧ q false, and r is true so ¬r is false.
¬r ∨ (p ∧ q) ≡ false ∨ false ≡ false
• r ⇒ (p ∨ q) ≡ ¬r ∨ (p ∨ q) = p ∨ q ∨ ¬r
In each of rows A, C, and E, at least one of p or q is true, so
p ∨ q ∨ ¬r = true
• (q ∧ r) ⇒ p ≡ ¬(q ∧ r) ∨ p ≡ (¬q ∨ ¬ r) ∨ p = p ∨ ¬q ∨ ¬r
In row E, p is false and both q and r are true, so ¬q and ¬r are both false.
false ∨ false ∨ false = false
• (q ∨ r) ⇒ p ≡ ¬(q ∨ r) ∨ p ≡ (¬q ∧ ¬r) ∨ p
In row E, p is false and both q and r are true, so both ¬q and ¬r are false.
(¬q ∧ ¬r) ∨ p ≡ (false ∧ false) ∨ false ≡ false ∨ false ≡ false
Answer:the last box
Step-by-step explanation:the other ones wouldnt make any sense
Two or more angles whose sum is 180° are called supplementary angles. The measure of the ∠y is 120°.
<h3>What are supplementary angles?</h3>
Two or more angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given the puck strikes the wall at an angle of 30°, it goes away at the same angle of 30°. Therefore, the measure of angle y can be found using the sum of the angle as a supplementary angle. Thus, we can write,
30° + ∠y + 30° = 180°
60° + ∠y = 180°
∠y = 180° - 60° = 120°
Hence, the measure of the ∠y is 120°.
Learn more about Supplementary Angles:
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Answer:
Below
Step-by-step explanation:
Area of a triangle :
Or , in simplified form :
Perimeter :
Answer:
91
Step-by-step explanation:
Let
x = first number
x+1 = second number
x+2 = third number
x+3 = fourth number
Total = 182
x + x + 1 + x + 2 + x + 3 = 182
4x + 6 = 182
Subtract 6 from both sides
4x + 6 - 6 = 182 - 6
4x = 176
Divide both sides by 4
x = 176 / 4
= 44
x = 44
x = 44
x+1 = 44 + 1 = 45
x+2 = 44 + 2 = 46
x+3 = 44 + 3 = 47
Sum of the two middle numbers = 45 + 46
= 91
