Question 34.How can i start to solve?
1 answer:
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I shall use the symbol U for union
^ for intersection
~ for complement
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The property of set subtraction states that for any sets X and Y, X-Y = X ^ Y~
That is in words, X throw away Y is the same as the intersection of X and the complement of Y
or X and anything NOT in Y
At the SET level, the proof looks like this:
(P-Q) U (Q-P) = « given
(P^Q~) U (Q ^ P~) = « property of set subtraction
(P U Q) ^ (P U P~) ^ (Q~ U Q) ^ (Q~ U P~) = « distributive property
(P u Q) ^ (Q~ U P~) = « Union of any set with it's complement is the universal
set which gets dropped by any intersection of a non-universal set
(P u Q ) ^ (Q ^ P)~ = « De Morgan's Law
(P u Q) - (Q ^ P) = « property of set subtraction
(P u Q) - (P ^ Q) « commutative property
<h3>----------------------------------------------------------------------------------------------------</h3>At the ELEMENT level, the proof looks like this:
» Proves left side is subset of right side
If x is in (P-Q) U (Q-P) then x is in (P-Q) OR x is in (Q-P)
If x is in P-Q then x is in P but not in Q.
Then X is in P U Q.
Since x is not in Q, x is NOT in P ^ Q
Hence x is in P U Q but NOT in P^Q, which
means it is an element if (P U Q) - (P ^ Q)
Therefore x is an element of the set defined by the right side, which means (P-Q) U (Q-P) is a subset of (P U Q) - (P ^ Q)
« proves right side is subset of the left side
If x is an element of (P U Q) - (P ^ Q) then
x is in (P U Q) but NOT in (P^Q)
Since x is in P U Q, x is in P OR x is in Q.
Since x is NOT in (P^Q) then x is NOT in BOTH P and Q.
Hence x is in either P or Q but not both.
If x is in P, then x is not in Q, so x is in P-Q.
Therefore x is in (P-Q) U (Q-P).if x is in Q, then x is not in P, so x is in Q-P.Therefore x is in (Q-P) U (P-Q).There x is an element of set defined by the left side, which menas (P u Q)-(P ^Q) is a subset of (P-Q) U (Q-P).
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Answer: Your answer is correct.
Explanation:
Use the marker gradations to identify the projected geometric shapes from the top, front and right side view as shown in the figure below.
All the gradation markings agree with your choice.
.
Explanation:
Use the marker gradations to identify the projected geometric shapes from the top, front and right side view as shown in the figure below.
All the gradation markings agree with your choice.
.