Translate the following conjunctions from symbols to words. Then, determine the truth value. p p : Ten is a whole number. q q q : Five is less than three. r r r : Two times seven is fourteen. p Λ p Λ p Λ ~ q Λ r q Λ r q Λ r .

Welcome back. In this problem, we'd like to translate P and not Q and R from symbols to words, and we've been given the simple statements P, Q, and R above. Now, let's start at the beginning with P. We're told P is a simple statement, 10 is a whole number. So, let's start there. 10 is a whole. Number Then we have this symbol which represents and. Then we have not Q. Now Q is 5 is less than 3, but we want not Q, so we can add in the word not to get the negation. 5 is not. Less than 3. We have another of these symbols, so that represents and, and we'll put and here. Finally, we have R, 2 times 7 is 14, so we'll write that in. 2 times 7 is 14. So we end up getting the statement, 10 is a whole number, and 5 is not less than 3, and 2 times 7 is 14. Now, this works. This is our conjunction, but we can also simplify it a bit. In English, when we're listing a bunch of things, instead of saying this and this and this, and saying the word and multiple times, we'll often use commas in place of some of those earlier ands. So we'll say this, comma, this comma, and this. We're going to simplify our conjunction here. And replace this first and with a comma, and then add a comma here. Now, again, our first answer wasn't wrong. This is just simpler, and it more accurately reflects how we would say this out loud. 10 is a whole number, 5 is not less than 3, and 2 times 7 is 14. Now that we have our conjunction, we want to determine if it is true. Now, a conjunction is true if each one of the statements we're combining together is true individually. Here, we are combining three statements together in a conjunction, so we need to check each of our three statements separately to see if they're all true, and the conjunction will only be true if all three of them are true on their own. Starting with 10 is a whole number. Well, 10 is a whole number, so this is true. Next, we have 5 is not less than 3, and 5 is not less than 3, so that's also true. And finally, we have 2 x 7 is 14. 2 times 7 is 14, so this is also true, because each of the three statements are true on their own, the conjunction combining them together is also going to be true. So we can say that P and not Q and R is true. Great work.

3. Logic

Logical Connectives

Quantitative Reasoning

3. Logic

Logical Connectives

Struggling with Quantitative Reasoning?

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Multiple Choice

Translate the following conjunctions from symbols to words. Then, determine the truth value.
$p$ : Ten is a whole number. $q$ : Five is less than three. $r$ : Two times seven is fourteen.
$p Λ$ ~ $q Λ r$ .

Ten is not a whole number, Five is not less than three, and Two times seven is fourteen; True

Ten is a whole number, Five is not less than three, and Two times seven is fourteen; False

Ten is not a whole number, Five is not less than three, and Two times seven is fourteen; False

Ten is a whole number, Five is not less than three, and Two times seven is fourteen; True

5:04m

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Struggling with Quantitative Reasoning?

Translate the following conjunctions from symbols to words. Then, determine the truth value.pp: Ten is a whole number. qqq: Five is less than three. rrr: Two times seven is fourteen.pΛp ΛpΛ~qΛrq Λ rqΛr.

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Translate the following conjunctions from symbols to words. Then, determine the truth value.
$p$ : Ten is a whole number. $q$ : Five is less than three. $r$ : Two times seven is fourteen.
$p Λ$ ~ $q Λ r$ .