233k views
4 votes
Which statements below are true?

A) If p q and r are true, then q + r is true.
B) If p + q and q r are true, then p is true.
C) If p q and q + r are true, then r is true.
D) If p q and p are true, then q is true.

1 Answer

6 votes

Final answer:

Among the provided statements, A and D are true, while B and C are false. Statement A is true because the disjunction of two true statements is true. Statement D is true because if a conjunction and one of its parts are true, the other part must also be true.

Step-by-step explanation:

The question is concerning the validity of logical statements and their relationships. Let's analyze each option:

  • A) If p, q, and r are true, then q + r is true. This statement is true because if q and r are individually true, their disjunction (represented symbolically as q + r) would also be true.
  • B) If p + q and q r are true, then p is true. This statement is false because p + q being true does not guarantee that p is true since the true value could come from q. Therefore, without additional information about q, we cannot conclude that p is true.
  • C) If p q and q + r are true, then r is true. This statement is false. Although q + r is true, it does not necessarily mean that r is true because q could be the true statement making the disjunction true.
  • D) If p q and p are true, then q is true. This statement is true. If p q (conjunction) is true and p is also true, then q must be true for the conjunction to hold.

Other examples in the provided information that demonstrate the property of truth are: the commutative property (A + B = B + A), which holds true for addition in mathematics, and the fact about independent events in probability (P(A AND B) = P(A)P(B) is true for independent events).

User Sudi
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories