Question Determine the truth value of $p \vee q$ , where $p: 6+5=11$ and $q: 7 \times 3=42$ . Choose the correct truth value: $p \vee q$ is true or $p \vee q$ is false.

Studdy Solution

STEP 1

Assumptions1. The statement $p$ is $6+5=11$ . The statement $q$ is $7 \times3=42$
3. The symbol $\vee$ represents the logical OR operator. The statement $p \vee q$ is true if either $p$ is true, or $q$ is true, or both are true.

STEP 2

First, we need to determine the truth value of the statement $p$ .
$p6+5=11$

STEP 3

Calculate the sum on the left side of the equation.
$6+5=11$

STEP 4

The sum of6 and is11, so the statement $p$ is true.

STEP 5

Next, we need to determine the truth value of the statement $q$ .
$q7 \times3=42$

STEP 6

Calculate the product on the left side of the equation.
$\times3=42$

STEP 7

The product of7 and3 is21, not42, so the statement $q$ is false.

STEP 8

Now that we have the truth values for $p$ and $q$ , we can determine the truth value for the statement $p \vee q$ .
$p \vee q = true \vee false$

STEP 9

According to the rules of the logical OR operator, the statement $p \vee q$ is true if either $p$ is true, or $q$ is true, or both are true. In this case, $p$ is true and $q$ is false, so $p \vee q$ is true.
The statement $p \vee q$ is true.

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Question Determine the truth value of $p \vee q$ , where $p: 6+5=11$ and $q: 7 \times 3=42$ . Choose the correct truth value: $p \vee q$ is true or $p \vee q$ is false.

Studdy Solution

STEP 1

Assumptions1. The statement $p$ is $6+5=11$ . The statement $q$ is $7 \times3=42$
3. The symbol $\vee$ represents the logical OR operator. The statement $p \vee q$ is true if either $p$ is true, or $q$ is true, or both are true.

STEP 2

First, we need to determine the truth value of the statement $p$ .
$p6+5=11$

STEP 3

Calculate the sum on the left side of the equation.
$6+5=11$

STEP 4

The sum of6 and is11, so the statement $p$ is true.

STEP 5

Next, we need to determine the truth value of the statement $q$ .
$q7 \times3=42$

STEP 6

Calculate the product on the left side of the equation.
$\times3=42$

STEP 7

The product of7 and3 is21, not42, so the statement $q$ is false.

STEP 8

Now that we have the truth values for $p$ and $q$ , we can determine the truth value for the statement $p \vee q$ .
$p \vee q = true \vee false$

STEP 9

According to the rules of the logical OR operator, the statement $p \vee q$ is true if either $p$ is true, or $q$ is true, or both are true. In this case, $p$ is true and $q$ is false, so $p \vee q$ is true.
The statement $p \vee q$ is true.

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Question Determine the truth value of p∨qp \vee qp∨q, where p:6+5=11p: 6+5=11p:6+5=11 and q:7×3=42q: 7 \times 3=42q:7×3=42. Choose the correct truth value: p∨qp \vee qp∨q is true or p∨qp \vee qp∨q is false.

Studdy Solution

STEP 1

Assumptions1. The statement ppp is 6+5=116+5=116+5=11 . The statement qqq is 7×3=427 \times3=427×3=423. The symbol ∨\vee∨ represents the logical OR operator. The statement p∨qp \vee qp∨q is true if either ppp is true, or qqq is true, or both are true.

STEP 2

First, we need to determine the truth value of the statement ppp.p6+5=11p6+5=11p6+5=11

STEP 3

Calculate the sum on the left side of the equation.6+5=116+5=116+5=11

STEP 4

The sum of6 and is11, so the statement ppp is true.

STEP 5

Next, we need to determine the truth value of the statement qqq.q7×3=42q7 \times3=42q7×3=42

STEP 6

Calculate the product on the left side of the equation.×3=42 \times3=42×3=42

STEP 7

The product of7 and3 is21, not42, so the statement qqq is false.

STEP 8

Now that we have the truth values for ppp and qqq, we can determine the truth value for the statement p∨qp \vee qp∨q.p∨q=true∨falsep \vee q = true \vee falsep∨q=true∨false

STEP 9

According to the rules of the logical OR operator, the statement p∨qp \vee qp∨q is true if either ppp is true, or qqq is true, or both are true. In this case, ppp is true and qqq is false, so p∨qp \vee qp∨q is true.The statement p∨qp \vee qp∨q is true.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Determine the truth value of $p \vee q$ , where $p: 6+5=11$ and $q: 7 \times 3=42$ . Choose the correct truth value: $p \vee q$ is true or $p \vee q$ is false.

Assumptions1. The statement $p$ is $6+5=11$ . The statement $q$ is $7 \times3=42$
3. The symbol $\vee$ represents the logical OR operator. The statement $p \vee q$ is true if either $p$ is true, or $q$ is true, or both are true.

First, we need to determine the truth value of the statement $p$ .
$p6+5=11$

Calculate the sum on the left side of the equation.
$6+5=11$

The sum of6 and is11, so the statement $p$ is true.

Next, we need to determine the truth value of the statement $q$ .
$q7 \times3=42$

Calculate the product on the left side of the equation.
$\times3=42$

The product of7 and3 is21, not42, so the statement $q$ is false.

Now that we have the truth values for $p$ and $q$ , we can determine the truth value for the statement $p \vee q$ .
$p \vee q = true \vee false$

According to the rules of the logical OR operator, the statement $p \vee q$ is true if either $p$ is true, or $q$ is true, or both are true. In this case, $p$ is true and $q$ is false, so $p \vee q$ is true.
The statement $p \vee q$ is true.