<em>p</em> … <em>q</em> … ¬<em>q</em> … <em>p</em> ∨ ¬<em>q</em> … (<em>p</em> ∨ ¬<em>q</em>) ⇒ <em>q</em>
T … T … F … T … T
T … F … T … T … F
F … T … F … F … T
F … F … T … T … F
Start with the first two columns, taking every possible pair of True/False for <em>p</em> and <em>q</em>.
¬<em>q</em> is just the negation of <em>q</em>, so True becomes False and False becomes True.
<em>p</em> ∨ <em>q</em> is the logical disjunction, or logical "or". It's True if either <em>p</em> or <em>q</em> is True, and False otherwise. So <em>p</em> ∨ ¬<em>q</em> is True only if either <em>p</em> or ¬<em>q</em> is True.
<em>p</em> ⇒ <em>q</em> is the logical implication. It's True only when both <em>p</em> and <em>q</em> are True, or when <em>p</em> is False. So (<em>p</em> ∨ ¬<em>q</em>) ⇒ <em>q</em> is True when both <em>p</em> ∨ ¬<em>q</em> and <em>q</em> are True, or when <em>p</em> ∨ ¬<em>q</em> is False.
Using the combination formula, it is found that there are 495 ways to choose a 4-topping sandwich.
The order in which the toppings are chosen is not important, hence the <em>combination formula</em> is used to solve this question.
<h3>What is the combination formula?</h3>
is the number of different combinations of x objects from a set of n elements, given by:
4 toppings are chosen from a set of 12, hence the number of ways is given by:
More can be learned about the combination formula at brainly.com/question/25821700
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Answer:
$480
Step-by-step explanation:
Perry makes 15% commission for each TV he sells.
How much would he have to sell a TV to get $72
First of all, let's call the unknown variable x
So 15% of x= $72
Mathematically, this would be represented as 15/100 * x= 72
15/100x= 72
Breaking down further,
15/100 can be broken down to 3/20
3/20x= 72
So to find the value of x, we divide both sides by 3/20
x= 72 ÷ 3/20
x= 72 * 20/3 (using the law of indices)
x= 1440/3
x= $480 dollars.
So, Perry would have to sell a TV for $480 to make a $72 commission.
Answer:
Step-by-step explanation:
Apply law of sines.
Given:
Kianas soccer teams ratio of wins to losses is 5:3.
Her team has played 24 games.
To find:
The number of games they won.
Solution:
Let the number of games they won be 5x and the number of games they lost be 3x.
Total number of games is 24.
Now, the number of games they won is:
Number of games they won =
=
=
Therefore, they won 15 games.