1.2. [2, 5]U[3, 7]=[2, 7]. EX LET x€[2,5]U[3,7]

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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End Prove

Prove
1.2.
[2, 5]U[3, 7] [2,7].
EX
LET
x€[2,5]U[3,7
[2,5]U[3,7]={x: xe[2,5]
= {2≤x≤5 V
AUB={x: XEA V XEB}
V xe[3,7]}
3≤x≤7}
[2,5] = [2, 3]U[3, 5].
= {2≤x≤3 V 3≤x≤5 V 3≤x≤7}
= {2≤x≤3 V 3≤x≤5 V 3≤x≤5 V 5≤x≤7}
p⇒ (p V p)
= {2≤x≤3 V 3≤x≤5 V 5≤x≤7}
= {(2≤x and x ≤3) V (3≤x
and
x <5) V (5≤x and x≤7)}
Transcribed Image Text:Prove 1.2. [2, 5]U[3, 7] [2,7]. EX LET x€[2,5]U[3,7 [2,5]U[3,7]={x: xe[2,5] = {2≤x≤5 V AUB={x: XEA V XEB} V xe[3,7]} 3≤x≤7} [2,5] = [2, 3]U[3, 5]. = {2≤x≤3 V 3≤x≤5 V 3≤x≤7} = {2≤x≤3 V 3≤x≤5 V 3≤x≤5 V 5≤x≤7} p⇒ (p V p) = {2≤x≤3 V 3≤x≤5 V 5≤x≤7} = {(2≤x and x ≤3) V (3≤x and x <5) V (5≤x and x≤7)}
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