false
Assuming that you mean not (p or q) if and only if P ~(PVQ)--> P so now construct a truth table, (just place it vertical since i cannot place it vertical through here.) P True True False False Q True False True False (PVQ) True True True False ~(PVQ) False False False True ~(PVQ)-->P True True True False if it's ~(P^Q) -->P then it's, P True True False False Q True False True False (P^Q) True False False False ~(P^Q) False True True True ~(P^Q)-->P True True False False
The expression ( p \land q ) is called the conjunction of ( p ) and ( q ). It represents the logical operation where the result is true only if both ( p ) and ( q ) are true. If either ( p ) or ( q ) is false, the conjunction ( p \land q ) is false.
In propositional logic, if we have statements p, q, and r, and we know that p is false, q is false, and r is true, the overall truth of a compound statement involving these variables would depend on the specific logical connectors used (such as AND, OR, NOT). For example, if the statement is "p AND q AND r," the result would be false, as both p and q are false. However, if the statement is "p OR q OR r," the result would be true because r is true. Thus, the truth value of the overall statement cannot be determined without knowing its specific form.
No, the statement "not(p and q)" is not equal to "(not p) or q." According to De Morgan's laws, "not(p and q)" is equivalent to "not p or not q." This means that if either p is false or q is false (or both), the expression "not(p and q)" will be true. Therefore, the two expressions represent different logical conditions.
The expression ( p \land q ) is called the "conjunction" of statements ( p ) and ( q ). It is true only when both ( p ) and ( q ) are true; otherwise, it is false. In logical terms, conjunction represents the logical AND operation.
Not sure I can do a table here but: P True, Q True then P -> Q True P True, Q False then P -> Q False P False, Q True then P -> Q True P False, Q False then P -> Q True It is the same as not(P) OR Q
Assuming that you mean not (p or q) if and only if P ~(PVQ)--> P so now construct a truth table, (just place it vertical since i cannot place it vertical through here.) P True True False False Q True False True False (PVQ) True True True False ~(PVQ) False False False True ~(PVQ)-->P True True True False if it's ~(P^Q) -->P then it's, P True True False False Q True False True False (P^Q) True False False False ~(P^Q) False True True True ~(P^Q)-->P True True False False
true or false = true
If p is true and q is false, p or q would be true. I had a hard time with this too but truth tables help. When using P V Q aka p or q, all you need is for one of the answers to be true. Since p is true P V Q would also be true:)
The statement "p if and only if q" is true when both p and q are true, or when both p and q are false.
The relational operators: ==, !=, =.p == q; // evaluates true if the value of p and q are equal, false otherwise.p != q; // evaluates true of the value of p and q are not equal, false otherwise.p < q; // evaluates true if the value of p is less than q, false otherwise.p q; // evaluates true if the value of p is greater than q, false otherwise.p >= q; // evaluates true of the value of p is greater than or equal to q, false otherwiseNote that all of these expressions can be expressed logically in terms of the less than operator alone:p == q is the same as NOT (p < q) AND NOT (q < p)p != q is the same as (p < q) OR (q < p)p < q is the same as p < q (obviously)p q is the same as (q < p)p >= q is the same as NOT (p < q)
In propositional logic, if we have statements p, q, and r, and we know that p is false, q is false, and r is true, the overall truth of a compound statement involving these variables would depend on the specific logical connectors used (such as AND, OR, NOT). For example, if the statement is "p AND q AND r," the result would be false, as both p and q are false. However, if the statement is "p OR q OR r," the result would be true because r is true. Thus, the truth value of the overall statement cannot be determined without knowing its specific form.
"P and not P" is always false. If P is true, not P is false; if P is false, not P is true. In either case, combining a true and a false with the AND operator gives you false. And if you look at the truth table for the implication (the "therefore" part), when the left part is false, the result is always true.
No, the statement "not(p and q)" is not equal to "(not p) or q." According to De Morgan's laws, "not(p and q)" is equivalent to "not p or not q." This means that if either p is false or q is false (or both), the expression "not(p and q)" will be true. Therefore, the two expressions represent different logical conditions.
The expression ( p \land q ) is called the "conjunction" of statements ( p ) and ( q ). It is true only when both ( p ) and ( q ) are true; otherwise, it is false. In logical terms, conjunction represents the logical AND operation.
Yes, because a variable cannot be both true and not true.
Let us consider "This statement is false." This quotation could also be read as "This, which is a statement, is false," which could by extent be read as "This is a statement and it is false." Let's call this quotation P. The statement that P is a statement will be called Q. If S, then R and S equals R; therefore, if Q, then P equals not-P (since it equals Q and not-P). Since P cannot equal not-P, we know that Q is false. Since Q is false, P is not a statement. Since P says that it is a statement, which is false, P itself is false. Note that being false does not make P a statement; all things that are statements are true or false, but it is not necessarily true that all things that are true or false are statements. In summary: "this statement is false" is false because it says it's a statement but it isn't.