Biconditional Math Example 3

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Example 3

easy
State whether each biconditional is true or false: (a) '3=3⇔5>23 = 3 \Leftrightarrow 5 > 2', (b) '3=4⇔1=23 = 4 \Leftrightarrow 1 = 2', (c) '3=3⇔1=23 = 3 \Leftrightarrow 1 = 2'.

Solution

  1. 1
    (a) T⇔T=TT \Leftrightarrow T = T.
  2. 2
    (b) F⇔F=TF \Leftrightarrow F = T.
  3. 3
    (c) T⇔F=FT \Leftrightarrow F = F.

Answer

(a)  T,(b)  T,(c)  F(a)\;T,\quad (b)\;T,\quad (c)\;F
A biconditional is true when both sides have the same truth value, even if both are false. It is only false when the truth values differ.

About Biconditional

A biconditional P↔QP \leftrightarrow Q is true when PP and QQ have the same truth value — both true or both false.

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More Biconditional Examples

Example 1 easy

Evaluate the biconditional [formula] for all truth value combinations and construct its truth table.

Example 2 medium

Determine whether '[formula] is even [formula] [formula] is even' is true for all integers [formula]

Example 4 medium

Verify that [formula] using a truth table.

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Related Concepts

Conditional Statement