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The logical operator OR, ||
This page introduces the logical operator OR.
In Java and some other languages the lpgical operator OR is written ||.
Jess wants to enrol in a course, but there are conditions for enrolment: a person can enrol if they have passed Maths 1 or if they have passed Stats 1. So Jess can enrol if
Jess has passed Maths 1 OR Jess has passed Stats 1
This tells you that:
- Jess has passed both Maths 1 and Stats 1 means that Jess can enrol.
- Jess passed Maths 1 but not Stats 1 means that Jess can enrol.
- Jess did not pass maths 1 but did pass Stats 1 means that Jess can enrol.
- Jess failed both means that Jess can't enrol.
We summarise this example in a table.
Passed Maths 1 | Passed Stats 1 | Allowed to Enrol |
---|---|---|
True | True | True |
True | False | True |
False | True | True |
False | False | False |
In general, || (OR) is used as shown in this truth table.
$a$ | $b$ | $a||b$ |
---|---|---|
T | T | T |
T | F | T |
F | T | T |
F | F | F |
In some places, for example some maths books, you might see the symbol $\lor$ used for the logical operator OR.
Example
Find the truth value of $24\gt 50||44-44=0$.
Answer: $\underbrace{24\gt 50}_{F}||\underbrace{44-44=0}_{T}$ is F||T, which is T. The answer is T.
Practice questions
Find the truth values of the following:
$1+1=2||42\gt 24$ | |
The capital city of Australia is Perth OR Western Sydney University is in Tasmania. | |
$42\gt 24||24\gt 42$ | |
$1=2||2\le 4$ |
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