Answer the following true or false. Justify your answer.
1 answer:
Answer:
a) False b) False c) True d) True e) True
Step-by-step explanation:
a) If A is a subset of B, and x∈B, then x∈A. False
Suppose A is Z (Set of Integers), and B is R (Set of Real Numbers). Then A is a subset of B. x ∈ B, let's say x equals π. If x ∈ B (B = Real Numbers) and x=π then x ∉ A (Z).
We could call A, any other subset of Real numbers (Q, I,..) and we both would come up to the same conclusion when it comes to Real numbers the Set.
So this conclusion is False. Not always an element of a subset is an element of a set.
b) False
For this one, I've drawn some lines, and it is useful to work with them.
Given the set {(x,y) ∈ R²| 0<x<0} then all negative and positive numbers but zero belong to this set.
c) If A and B are square matrices, then AB is also square. True
Taking into account the rules for multiplying matrices. The number of columns of A must be the same number of lines of B to there can be a matrix product.
Whenever we multiply square matrices, we'll always get square matrices. Then this conclusion is true.
d) A and B are subsets of a set S, then A∩B and A∪B are also subsets of S. True
Suppose A= Z (Integer Numbers) and B=Q (Rational Numbers) and S= R (Real Numbers)
A∩B = Z∩Q=∅ and A∪B =Z∪Q = subset
Since the ∅ empty set ⊂ in every set and ZUQ is another Subset of R this is a True conclusion.
e) True. For a matrix A, we define A²= AA
For any Power of Matrices, all we have to do is multiply any given matrix by itself for a given number of times.
M²=M*M
M³=M*M*M
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Answer:
Rayshawn originally had $30.
Step-by-step explanation:
i) Rayshawn has a certain amount of money. Let us say this amount is $x.
ii) Rayshawn spends $20 which means that he is left with $(x - 20)
iii) it is also given that amount of money left after spending $20 is of the original amount, $x, the amount remaining is
.
iv) from the information given in ii) and iii) we get
$(x - 20) = , Therefore we get 3x - 60 = x , therefore 2x = 60,
Therefore x = $30. Rayshawn originally had $30.
Answer:
We can expect 8255 numbers of students are liberal arts majors.
Step-by-step explanation:
Given:
Total Number of students in the college = 8943
Now According to Mr. Jones Survey;
60 out of 65 students are liberal arts majors.
We need to find the number of students who are liberal arts majors out of total number of students in college.
Solution:
First we will find the Percentage number of students who are liberal arts majors according to survey.
Percentage number of students who are liberal arts majors can be calculated by dividing 60 from 65 then multiplying by 100.
framing above quote in equation form we get;
Percentage number of students who are liberal arts majors =
Now we will find the Total number of students who are liberal arts major.
Total number of students who are liberal arts major can be calculated by Multiplying Percentage number of students who are liberal arts majors with total number of students in the college and then dividing by 100.
framing above quote in equation form we get;
Total number of students who are liberal arts major =
Since number of students cannot be in point, so we will round the value.
Hence We can expect 8255 numbers of students are liberal arts majors.