Determine whether p ∧ (p → q) and p ∧ q are logically equivalent.
1 answer:
Answer:
Yes they are logically equivalent
p∧(p→q)≡p∧q
Step-by-step explanation:
The statements are logically equivalent if they have the same truth tables. So let´s use truth tables in order to determine if they are logically equivalent or not:
The picture that I attached you shows the truth table for each case. As you can see, p∧(p→q) has exactly the same truth values as p∧q. So we can conclude that they are logically equivalent.
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Answer:
Step-by-step explanation:
The first step to solve the exercise is to make the conversion from meters to centimeters.
Since , then the dimensions of the wood board in centimeters are:
Now, you must find the Greatest Common Factor (GCF). The steps are:
- Descompose 100 and 60 into their prime factors:
- Multiply the commons with the lowest exponents:
Therefore, the side lenght of each square must be:
We have to find the expected value for the PlayBall lottery.
The price of the ticket = $1
Prize amount = $250
If a player wins, he will be winning $249 as the price is not paid back along with the prize amount. He is spending $1, getting back $250, so the net amount he is getting back is $249.
Now we have to find the probability of winning and losing.
Number of letters from A to T = 20
Number of digits from 0 to 9 = 10
Probability of picking up the same letter that was picked on that day = 1/20
Probability of picking up the same number that was picked on that day = 1/10
Thus, the Probability of picking up the same letter and same number that was picked on that day =
Thus, the probability of winning = 1/200
The probability of losing =
The expected value E for the PlayBall lottery will be:
Thus, the option C gives the correct answer
The price of the ticket = $1
Prize amount = $250
If a player wins, he will be winning $249 as the price is not paid back along with the prize amount. He is spending $1, getting back $250, so the net amount he is getting back is $249.
Now we have to find the probability of winning and losing.
Number of letters from A to T = 20
Number of digits from 0 to 9 = 10
Probability of picking up the same letter that was picked on that day = 1/20
Probability of picking up the same number that was picked on that day = 1/10
Thus, the Probability of picking up the same letter and same number that was picked on that day =
Thus, the probability of winning = 1/200
The probability of losing =
The expected value E for the PlayBall lottery will be:
Thus, the option C gives the correct answer