Practice Or Statements (Disjunction) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A disjunction is a compound statement that is true whenever at least one of its parts is true.
At least one must be true. Logical OR is inclusive — "P or Q or both" — unlike the exclusive everyday "either/or."
Showing a random 20 of 50 problems.
Example 1
easyEvaluate: ' OR '.
Example 2
medium ____ (identity law).
Example 3
challengeHow many of the rows make true, and why?
Example 4
hardProve via truth table.
Example 5
mediumSolve '' and explain why the answer is naturally an OR.
Example 6
mediumUse a truth table to verify De Morgan's Law: .
Example 7
mediumTranslate to symbols: 'It is raining or it is snowing'. Use for raining, for snowing.
Example 8
easyIf both and are true, what is (inclusive or)?
Example 9
mediumIf is true and is false, what must be?
Example 10
hardOut of 80 students, 50 take Spanish, 35 take French, and 20 take both. How many take Spanish OR French?
Example 11
easyIf is false and is true, what is ?
Example 12
mediumIs logically equivalent to ?
Example 13
mediumIf is false, what are and ?
Example 14
mediumEvaluate '' where : ' is even' and : ' is prime'.
Example 15
easyIn set notation, ' OR ' is equivalent to ____ .
Example 16
easyIf is true and is false, what is ?
Example 17
mediumSolve and write the solution as a disjunction.
Example 18
mediumFind all real satisfying ' or ', and express as a union of intervals.
Example 19
hardAmong the 16 possible truth functions of two variables, how many are true on at least one of the four rows? (Disjunction is one of them.)
Example 20
mediumBuild the truth table column for and identify the familiar connective it equals.