Conjunction Math Example 4

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

Example 4

medium
Simplify: find all x∈Rx \in \mathbb{R} satisfying 'x>1x > 1 and x<4x < 4', and express as an interval.

Solution

  1. 1
    The condition is x>1x > 1 AND x<4x < 4, i.e., both must hold simultaneously.
  2. 2
    This means 1<x<41 < x < 4, which in interval notation is (1,4)(1, 4).

Answer

x∈(1,4)x \in (1, 4)
A compound inequality joined by 'and' requires both conditions to hold at once. The solution is the intersection of the two individual solution sets (1,∞)∩(−∞,4)=(1,4)(1,\infty) \cap (-\infty,4) = (1,4).

About Conjunction

A conjunction P∧QP \wedge Q is a compound statement that is true if and only if both constituent statements PP and QQ are individually true.

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More Conjunction Examples

Example 1 easy

Let [formula]: '[formula] is even' and [formula]: '[formula]'. Evaluate [formula], [formula], and [f

Example 2 medium

Construct the full truth table for [formula] and use it to show that conjunction is commutative: [fo

Example 3 easy

Determine the truth value of: (a) '[formula] and [formula]', (b) '[formula] and [formula]'.

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