If p is true and ~ q is false, then p ~ q is always, sometimes, never false.
1 answer:
Answer:
never
Step-by-step explanation:
The expression: ~q means "not q"
If ~q is false, then q is true
The expression:
If p is true and ~q is false
is equivalent to:
If p is true and q is true
then:
If p is true and q is true, then p -> q is <u>never</u> false (or is always true, see table attached). Or:
If p is true and ~q is false, then p -> ~q is <u>never</u> false.
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A student had 500 milliliters of water in a water bottle. She drank 25% of the water before soccer practice. After practice, she drank 1/3 of the remaining water.
How much water, in milliliters, does the student have left in the bottle?
Answer:
the amount of water the student have left in the bottle is 250 milliliters
Step-by-step explanation:
A student had 500 milliliters of water in a water bottle. She drank 25% of the water before soccer practice. After practice, she drank 1/3 of the remaining water.
How much water, in milliliters, does the student have left in the bottle?
Before the soccer practice, she drank 25 % of the water
25% of the water = 25% of 500
= 25% × 500
= × 500
At the right hand-side of the equation, the two zeros will cancel-out the other two zeros, hence;
= 25 × 5
=125
25% of the water = 125 milliliters
From the question, it was said that drank 25% of the water before soccer, this implies that she drank 125 milliliters from the water bottles.
If she drank 125 milliliters of from a 500 milliliters water contain in the water bottle, then the amount of water left will be 500 ml - 125 ml = 375 ml
This implies that before the soccer practice she had 375 milliliters of water left in the water bottle.
After the practice, she drank 1/3 of the remaining water, which means after the practice she drank 1/3 of 375
1/3 of 375 = × 375 =
= 125
After the practice she drank 125 milliliters of water from her 375 milliliters water.
The amount of water she have left after the practice will be;
375 milliliters - 125 milliliters = 250 milliliters
Therefore, the amount of water the student have left in the bottle is 250 milliliters
Answer:
(A) Set A is linearly independent and spans . Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors , we are to decide which of the given statements is true:
In Matrix , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans . Thus it is basis for
.