1.2. [2, 5]U[3, 7]=[2, 7]. EX LET x€[2,5]U[3,7]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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)}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96d6b0bc-8bd5-480b-b82f-d2768f6edf2a%2F562def27-a164-4efd-baad-61ec081b11c1%2Frmho40o_processed.png&w=3840&q=75)
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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