If P ≤ Q and Q < R, which of the following is true?

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Question: If P ≤ Q and Q < R, which of the following is true?

Options:

Correct Answer: P < R

Solution:

Since P ≤ Q and Q < R, it follows that P < R.

If P ≤ Q and Q < R, which of the following is true?

If P ≤ Q and Q < R, which of the following is true?

Step 1: Understand the symbols. 'P ≤ Q' means P is less than or equal to Q. 'Q < R' means Q is less than R.
Step 2: Since P is less than or equal to Q, we can say that P is either equal to Q or less than Q.
Step 3: Since Q is less than R, we know that Q is not equal to R.
Step 4: If P is equal to Q, then P is still less than R because Q is less than R.
Step 5: If P is less than Q, then P is also less than R because Q is less than R.
Step 6: In both cases (whether P is equal to Q or less than Q), we conclude that P is less than R.
Step 7: Therefore, we can say that P < R is true.

Inequalities – Understanding the relationships between numbers using inequalities (≤ and <) and how they can be combined.
Transitive Property – Applying the transitive property of inequalities, which states that if a ≤ b and b < c, then a < c.