End Prove Prove1.2.[2, 5]U[3, 7] [2,7].EXLETx€[2,5]U[3,7[2,5]U[3,7]={x: xe[2,5]= {2≤x≤5 VAUB={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≤xandx <5) V (5≤x and x≤7)}

Answered: 1.2. [2, 5]U[3, 7]=[2, 7]. EX LET…

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)}

Expert Solution

Step 1: Two sided proof of Set:

To complete the proof, one must find that

$... c o n t d equals left curly bracket 2 less or equal than x space a n d space left parenthesis space x less or equal than 3 space logical or x less or equal than 5 logical or x less or equal than 7 right parenthesis right curly bracket equals left curly bracket 2 less or equal than x space a n d space x less or equal than 7 right curly bracket B u t space i t space i m p l i e s space x element of left square bracket 2 comma 7 right square bracket H e n c e comma space left square bracket 2 comma 5 right square bracket union left square bracket 3 comma 7 right square bracket subset of or equal to left square bracket 2 comma 7 right square bracket$