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.
"\\lnot p" is a negation of "p". Statement "\\lnot p" is: "4" is an irrational number. This statement is false.
"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.
"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.
"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.
"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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