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secondary 4 | E Maths
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Date Posted: 3 years ago
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Not sure if this is correct but hope it helps
Date Posted:
3 years ago
(i) will actually include everything because we count everything which is inside P or outside Q - which technically covers the entire space (and we are in fact double counting the doughnut region).
(ii) is correct - it must be inside P AND outside Q at the same time.
(iii) is correct - we only count the region outside of the combination of all possible regions in P or Q.
(iv) is correct - we count all the regions which is outside of the intersecting region of P and Q.
(ii) is correct - it must be inside P AND outside Q at the same time.
(iii) is correct - we only count the region outside of the combination of all possible regions in P or Q.
(iv) is correct - we count all the regions which is outside of the intersecting region of P and Q.
(v) is correct - we count all the possible regions which are outside P or outside Q, so we do not include the inner circle. As a matter of fact, (P u Q)' is the same as P' n Q'.
(vi) is correct - we only count only the common region which is outside P and outside Q, and this must be entirely outside P. As a matter of fact, (p n Q)' is the same as P' u Q'.
(vii) is correct. P' u Q means combining the region outside P with the region inside Q, so (P' u Q)' means the region which is not described yet (the doughnut region)/
(viii) should not contain any shaded region at all. P u Q' means combining the region inside P with the region outside Q, which technically covers the entire space. So, (P u Q')' will be none of the regions since P u Q' covers every region.
(vi) is correct - we only count only the common region which is outside P and outside Q, and this must be entirely outside P. As a matter of fact, (p n Q)' is the same as P' u Q'.
(vii) is correct. P' u Q means combining the region outside P with the region inside Q, so (P' u Q)' means the region which is not described yet (the doughnut region)/
(viii) should not contain any shaded region at all. P u Q' means combining the region inside P with the region outside Q, which technically covers the entire space. So, (P u Q')' will be none of the regions since P u Q' covers every region.
Here's a guide to working with set notations:
P = Everything in P
Q = Everything in Q
P' [pronounced P prime] = Everything not in P
Note: P' is also known as the 'complement'
U = union of sets [basically, addition]
P U Q = Everything in P and everything in Q
P' U Q = Everything not in P and everything in Q
n = intersect [both must have]
P n Q = Everything that is in both P AND Q
P n Q' = Everything that is in both P AND not in Q
When you have complex sets like (P' U Q)' for instance, identify what the inside parts are first in terms of shaded area, then just apply the complement next (i.e. shaded becomes unshaded, unshaded becomes shaded).
Breaking your sets down into pieces can help you not get overwhelmed by them.
P = Everything in P
Q = Everything in Q
P' [pronounced P prime] = Everything not in P
Note: P' is also known as the 'complement'
U = union of sets [basically, addition]
P U Q = Everything in P and everything in Q
P' U Q = Everything not in P and everything in Q
n = intersect [both must have]
P n Q = Everything that is in both P AND Q
P n Q' = Everything that is in both P AND not in Q
When you have complex sets like (P' U Q)' for instance, identify what the inside parts are first in terms of shaded area, then just apply the complement next (i.e. shaded becomes unshaded, unshaded becomes shaded).
Breaking your sets down into pieces can help you not get overwhelmed by them.
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