Determine the number of outcomes in the event. Decide whether the event is a simple event or not. A computer is used to select r
1 answer:
The probability of selecting a number greater than 8 will be .
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The number of outcomes = { 1,2,3,4,5,6,7,8,9 } = Counts = 9
Favourable outcomes = { 9 } = counts = 1
The probability will be given as:-
Therefore the probability of selecting a number greater than 8 will be .
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First, we must solve for the radius of the sphere:
V=
r=(3
)
r=(3*
)
r≈5.99
Second, we must solve for surface area:
A=4
A=4**
A≈450.88
V=
r=(3
r=(3*
r≈5.99
Second, we must solve for surface area:
A=4
A=4*
A≈450.88
Answer:
For the set X = {a, b, c}, the following three relations satisfy the required conditions in (a), (b) and (c) respectively.
(a) R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)} is reflexive and symmetric but not transitive .
(b) R = {(a, a), (b, b), (c, c), (a, b)} is reflexive and transitive but not symmetric .
(c) R = {(a,a), (a, b), (b, a)} is symmetric and transitive but not reflexive .
Step-by-step explanation:
Before, we go on to check these relations for the desired properties, let us define what it means for a relation to be reflexive, symmetric or transitive.
Given a relation R on a set X,
R is said to be reflexive if for every .
R is said to be symmetric if for every .
R is said to be transitive if and
, then
.
(a) Let R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)}.
Reflexive:
Therefore, R is reflexive.
Symmetric:
Therefore R is symmetric.
Transitive: but but (a,c) is not in R.
Therefore, R is not transitive.
Therefore, R is reflexive and symmetric but not transitive .
(b) R = {(a, a), (b, b), (c, c), (a, b)}
Reflexive:
Therefore, R is reflexive.
Symmetric:
Therefore R is not symmetric.
Transitive: and
.
Therefore, R is transitive.
Therefore, R is reflexive and transitive but not symmetric .
(c) R = {(a,a), (a, b), (b, a)}
Reflexive: but (b, b) and (c, c) are not in R
R must contain all ordered pairs of the form (x, x) for all x in R to be considered reflexive.
Therefore, R is not reflexive.
Symmetric: and
Therefore R is symmetric.
Transitive: and
.
Therefore, R is transitive.
Therefore, R is symmetric and transitive but not reflexive .