Difference between revisions of "Conditional"
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− | A conditional is used in [[logic]] for two statements. When the statements are represented by [[variable|variables]], the variables usually are p, q, and so forth. An example of a conditional using p and q would be denoted <math>p \rightarrow q</math> and read "if p, then q." The first statement, p, is called the [[antecedent]] while the second statement, q, is called the [[consequent]]. A conditional is considered true when the antecedent and consequent are both true or if the antecedent is false. When the antecedent is false, the [[truth value]] of the consequent does not matter; the conditional will always be true. A conditional is considered false when the antecedent is true and the consequent is false. Below, the truth values of the conditional for all possibilities of the antecedent and consequent being true or false are represented in a [[truth table]]. | + | A conditional is used in [[logic]] for two statements. When the statements are represented by [[variable|variables]], the variables usually are p, q, and so forth. An arrow represents the conditional. An arrow with one shaft and two shafts are both widely used. An example of a conditional using p and q would be denoted <math>p \rightarrow q</math> or <math> p \Rightarrow q</math> and read "if p, then q." The first statement, p, is called the [[antecedent]] while the second statement, q, is called the [[consequent]]. A conditional is considered true when the antecedent and consequent are both true or if the antecedent is false. When the antecedent is false, the [[truth value]] of the consequent does not matter; the conditional will always be true. A conditional is considered false when the antecedent is true and the consequent is false. Below, the truth values of the conditional for all possibilities of the antecedent and consequent being true or false are represented in a [[truth table]]. |
− | {| | + | {| |
− | |+ Truth | + | |+ Truth table for a conditional |
− | ! ''P'' | + | !width="50"|''P'' |
− | |- | + | !width="50"|''Q'' |
− | | | + | !width="75"|''P'' ⇒ ''Q'' |
− | |- | + | |- align="center" |
− | | | + | | T || T || T |
− | |- | + | |- align="center" |
− | | | + | | T || F || F |
− | |- | + | |- align="center" |
− | | | + | | F || T || T |
+ | |- align="center" | ||
+ | | F || F || T | ||
|} | |} |
Revision as of 01:14, 1 July 2006
A conditional is used in logic for two statements. When the statements are represented by variables, the variables usually are p, q, and so forth. An arrow represents the conditional. An arrow with one shaft and two shafts are both widely used. An example of a conditional using p and q would be denoted or and read "if p, then q." The first statement, p, is called the antecedent while the second statement, q, is called the consequent. A conditional is considered true when the antecedent and consequent are both true or if the antecedent is false. When the antecedent is false, the truth value of the consequent does not matter; the conditional will always be true. A conditional is considered false when the antecedent is true and the consequent is false. Below, the truth values of the conditional for all possibilities of the antecedent and consequent being true or false are represented in a truth table.
P | Q | P ⇒ Q |
---|---|---|
T | T | T |
T | F | F |
F | T | T |
F | F | T |