Answer to Question #331324 in Discrete Mathematics for che

Question #331324

A. Let p and q be propositions


p: 4 is a rational number


q: 3 is an irrational number.



Express each of these propositions as an English sentence:


1. ¬p =


2. p v q =


3. p ^ q =


4. p→q =


5. p ↔q =




1
Expert's answer
2022-04-21T03:29:14-0400

Statement "p" is true. Statement "q" is false.

  1. "\\lnot p" is a negation of "p". Statement "\\lnot p" is: "4" is an irrational number. This statement is false.
  2. "p\\lor q" is disjunction of "p" and "q". The statement "p\\lor q" is: 4 is a rational number or 3 is an irrational number. The latter statement is true.
  3. "p\\land q" is a conjunction of "p" and "q". The statement "p\\land q" is: 4 is a rational number and 3 is an irrational number. The latter statement is false.
  4. "p\\rightarrow q" is a material implication from "p" to "q". The statement "p\\rightarrow q" is: From the fact that 4 is a rational number it follows that "3" is an irrational number. This statement is false.
  5. "p\\leftrightarrow q" is the logical biconditional. The statement "p\\leftrightarrow q" is: The statement "4 is a rational number" holds if and only if the statement "3 is an irrational number" holds. The latter statement is false.

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