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:
3
Step-by-step explanation:
Remember the order of operations using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). So, you get 18 - 6 / 5-1 = 12/4 = 3
E: 36 because the total degrees of a parallelogram is 360 and opposite angles of parallelogram’s are equal so the angles diagonal from the given ones are the same. So the corners are 3x, 2x, 3x, 2x. In total that is 10x. 360/10 = 36
Answer:
And we can find this probability using excel or the normal standard tabe and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using excel or the normal standard tabe and we got:
Answer:
2.
Step-by-step explanation:
The gradient or slope of a straight line which is found between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Where y2 = 7
y1 = 3
x2 = 4
x1 = 2
=> m = (7 - 3) / (4 - 2)
m = 4 / 2 = 2
The gradient is 2.
