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).
Answer:
1
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 4-2)/(1 - -1)
= (4-2)/(1+1)
= 2/2
= 1
Answer:
(1, 2)
Step-by-step explanation:
Subtract the second equation from the first:
(y) -(y) = (6x -4) -(-x +3)
0 = 7x -7 . . . . . simplify
0 = x - 1 . . . . . . divide by 7
1 = x . . . . . . . . . add 1
y = -1 +3 = 2 . . . substitute into the second equation
The solution is (x, y) = (1, 2).
Answer:
The answer is a
Step-by-step explanation:
Using point (0,0) and (3,-9)
Slope of the line = -9-0/3-0 = -9/3 = -3
Equation of the line using point (0,0)
y - 0 = -3(x -0)
y= -3x
Hope this helps.
Answer:
Step-by-step explanation:
Given:
< C = 53°
< B = 80°
a = 2
Required:
Find b
Solution:
The question given suggests we are given measures for a ∆.
To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.
=> A = 180 - (53 + 80) = 47°
Law of Sines: 
Plug in the values into the formula
Cross multiply
Divide both sides by sin(47) to make b the subject of formula
(nearest tenth)
