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2 answers:
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Answer:
0.3 galloons of water.
Step-by-step explanation:
We know that 1/5 galloons of water fills 2/3 of the bin.
So, we can write the following fraction:
We want to find how many galloons will fill the entire bin or 1 whole bin. So, we can write the following proportion:
To find our answer, we need to solve for x.
So, let's cross-multiply. This yields:
Multiply both sides by 3:
The left side simplifies. Multiply on the right:
Now, multiply both sides by 1/2:
Simplify the left. Multiply on the right:
So, 3/10 of 0.3 of a gallon of water will fill the entire bin.
And we're done!
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 .