Question

For each question, use the following statements to write the compound statement anddetermine its truth value.P: Perpendicular lines intersect to form right angles.Q: All eagles are bald eagles.R: The capital of Texas is Houston.S: Congruent segments have equal length.Write the compound statement and determine its truth value: R^~RThe capital of Texas is Houston or the capital of Texas is not Houston; trueThe capital of Texas is Houston and the capital of Texas is not Houston; trueThe capital of Texas is Houston or the capital of Texas is not Houston; falseThe capital of Texas is Houston and the capital of Texas is not Houston;false

Answer 1

Answer

Option A is correct.

(R)^(~R) : The capital of Texas is Houston or the capital of Texas is not Houston; true

Explanation

We've been given a couple of statement.

We are then asked to use these statements to form compound statements and determine its truth value.

The one given in this question is,

(R)^(~R)

Note that,

R: The capital of Texas is Houston.

So,

~R: The capital of Texas is not Houston.

And,

(R)^(~R) mean R or ~R.

So,

(R)^(~R): The capital of Texas is Houston or the capital of Texas is not Houston

But to check the truth element.

The true capital of Texas is Austin.

Hence, R: The capital of Texas is Houston is False.

And ~R: The capital of Texas is not Houston is True.

(R)^(~R) = False or True = True. (According to logic gates)

Hope this Helps!!!