Why is the statement if/p then q true when p is false and q is true?
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Why is the statement if/p then q true when p is false and q is true?
Conditional Propositions – A statement that proposes something is true on the condition that something else is true. For example, “If p then q”* , where p is the hypothesis (antecedent) and q is the conclusion (consequent). This Disjunction is False because both propositions are false.
Is true when both p and q are true and is false otherwise?
The proposition “p and q,” denoted by pq is true when both p and q are true and is false otherwise. This is called the conjunction of p and q. Let p and q be propositions. The proposition “p or q,” denoted by pq, is the proposition that is false when p and q are both false and true otherwise.
Why is if false then true true?
5 Answers. As an example of why the convention ‘false implies true is true’ is useful, consider the sentence “if a given number is smaller than 10 then it is also smaller than 100”. This is clearly a true statement. This is an example of ‘false implies true’, and it still should be a true statement.
Why is true implies false false?
So the reason for the convention ‘false implies true is true’ is that it makes statements like x<10→x<100 true for all values of x, as one would expect. You want “real life”, eh? If the policeman sees you speeding, then you will have to pay a fine. This is true.
Which statement is always true when p is false?
5 Cards in this Set
| A compound statement that is always true is called a/an | Tautology |
|---|---|
| A biconditional statement p <->q is true when? | P and q have the same truth value |
| Determine whether the statement is true or false. “Some implications are not tautologies “ | False all implications are tautologies |
What is the truth table of P and Q?
So because we don’t have statements on either side of the “and” symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p….Truth Tables.
| p | q | p∧q |
|---|---|---|
| T | F | F |
| F | T | F |
| F | F | F |