Disjunction Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Evaluate: (a) 'F ∨\lor T', (b) 'F ∨\lor F', (c) 'T ∨\lor T'.

Solution

  1. 1
    (a) F∨T=TF \lor T = T (at least one is true).
  2. 2
    (b) F∨F=FF \lor F = F (neither is true).
  3. 3
    (c) T∨T=TT \lor T = T (at least one, in fact both, are true).

Answer

(a)  T,(b)  F,(c)  T(a)\;T,\quad (b)\;F,\quad (c)\;T
Disjunction is false only when both components are false. All other combinations yield true.

About Disjunction

A disjunction P∨QP \vee Q is a compound statement that is true whenever at least one of its parts is true.

Learn more about Disjunction →

More Disjunction Examples

Example 1 easy

Let [formula]: '[formula] is even' and [formula]: '[formula] is odd'. Evaluate [formula] and explain

Example 2 medium

Find all real [formula] satisfying '[formula] or [formula]', and express as a union of intervals.

Example 4 medium

Use a truth table to verify De Morgan's Law: [formula].

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