Let p be "it is raining" and q be "the track meet will be canceled." write p->q in words

Mathematics

1 answer:

trasher [3.6K]3 years ago

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The statement for the logic $\text{p}\rightarrow\text{q}$ is $\fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}$

Further explanation:

The logic given in the question is $\text{p}\rightarrow\text{q}$ .

The logic $\text{p}\rightarrow\text{q}$ is a symbol of implication.

Statement p is “It is raining” and the statement q is “The track meet will be canceled”.

The statement formed for the logic $\text{p}\rightarrow\text{q}$ is called a compound statement.

The truth table for the logic $\text{p}\rightarrow\text{q}$ is attached below.

From the table attached below it is observed that there are four cases for the compound statement.

Case1:

If p statement is true and the q statement is true then the compound statement for $\text{p}\rightarrow\text{q}$ is also true.

Case 2:

If p statement is true and the q statement is false then the compound statement for $\text{p}\rightarrow\text{q}$ is false.

Case 3:

If p statement is false and the q statement is true then the compound statement for $\text{p}\rightarrow\text{q}$ is true.

Case 4:

If p statement is false and the q statement is false then the compound statement for $\text{p}\rightarrow\text{q}$ is true.

For a true statement it can also be said that it is a positive statement and for a false statement it can be said that it is a negative statement.

Statement p is given as “It is raining”, which is a positive statement or a true statement.

Statement q is given as “The track meet will be cancelled”, which is a positive statement or a true statement.

As per the table attached for the logic $\text{p}\rightarrow\text{q}$ it is observed that the given statements p and q resembles with the case $1$ as both of the statement are true.

So, the compound statement for $\text{p}\rightarrow\text{q}$ is also a true statement.

The compound statement for the logic $\text{p}\rightarrow\text{q}$ is as follows:

$\fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}$

Therefore, the compound statement for the logic $\text{p}\rightarrow\text{q}$ is $\fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}$

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