6. Which of the following statements are always true, for any sets A and B? (Hint: try a few examples for A and B to see what is true. Also, you might compare P(A+B) and P(A)P(B), as in the previous exercise.) (i) if A ≤ B, then P(A) = P(B) (ii) if A ≤ B, then |P(A)| ≤ IP(B)| = (iii) |AB| |A|+|B| = (iv) |AB| |A|+|B|-|ANBI = (v) |AUB||A|+|B|-|ANBI (vi) |ANBI ≤IA BI (vii) P(AUB) = P(A) U P(B) U P(ANB) (viii) P(A+B) = (P(A) U P(B)) - P(ANB) (ix) P(A+B) = P(AUB) - P(ANB) (x) P(A)P(B) = (P(A) u P(B)) - P(ANB) (xi) P(A)P(B) = P(AUB) - P(ANB) 0/5
6. Which of the following statements are always true, for any sets A and B? (Hint: try a few examples for A and B to see what is true. Also, you might compare P(A+B) and P(A)P(B), as in the previous exercise.) (i) if A ≤ B, then P(A) = P(B) (ii) if A ≤ B, then |P(A)| ≤ IP(B)| = (iii) |AB| |A|+|B| = (iv) |AB| |A|+|B|-|ANBI = (v) |AUB||A|+|B|-|ANBI (vi) |ANBI ≤IA BI (vii) P(AUB) = P(A) U P(B) U P(ANB) (viii) P(A+B) = (P(A) U P(B)) - P(ANB) (ix) P(A+B) = P(AUB) - P(ANB) (x) P(A)P(B) = (P(A) u P(B)) - P(ANB) (xi) P(A)P(B) = P(AUB) - P(ANB) 0/5
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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Transcribed Image Text:6. Which of the following statements are always true, for any sets A and B?
(Hint: try a few examples for A and B to see what is true. Also, you might
compare P(A+B) and P(A)P(B), as in the previous exercise.)
(i) if A ≤ B, then P(A) = P(B)
(ii) if A ≤ B, then |P(A)| ≤ IP(B)|
=
(iii) |AB| |A|+|B|
=
(iv) |AB| |A|+|B|-|ANBI
=
(v) |AUB||A|+|B|-|ANBI
(vi) |ANBI ≤IA BI
(vii) P(AUB) = P(A) U P(B) U P(ANB)
(viii) P(A+B) = (P(A) U P(B)) - P(ANB)
(ix) P(A+B) = P(AUB) - P(ANB)
(x) P(A)P(B) = (P(A) u P(B)) - P(ANB)
(xi) P(A)P(B) = P(AUB) - P(ANB)
0/5
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