Respuesta :
Answer:
A and C
Step-by-step explanation:
To determine which events are equal, we explicitly define the elements in each set builder.
For event A
A={1.3}
for event B
B={x|x is a number on a die}
The possible numbers on a die are 1,2,3,4,5 and 6. Hence event B is computed as
B={1,2,3,4,5,6}
for event C
[tex]C=[x|x^{2}-4x+3]\\solving x^{2}-4x+3\\x^{2}-4x+3=0\\x^{2}-3x-x+3=0\\x(x-3)-1(x-3)=0\\x=3 or x=1[/tex]
Hence the set c is C={1,3}
and for the set D {x| x is the number of heads when six coins re tossed }
In the tossing a six coins it is possible not to have any head and it is possible to have head ranging from 1 to 6
Hence the set D can be expressed as
D={0,1,2,3,4,5,6}
In conclusion, when all the set are compared only set A and set C are equal
The events which are equal are (a) A = {1,3} and (c) C = {x | x2 −4x +3=0 }
Equal Sets
Equal sets are defined as the sets that have the same cardinality and all equal elements
Now, we will determine which of the given sets are equal
- For (a) A = {1,3}
The elements have been given
- For (b) B = {x | x is a number on a die }
The numbers on a die are 1, 2, 3, 4, 5, and 6
∴ B = {1, 2, 3, 4, 5, 6}
- For (c) C = {x | x² −4x +3=0 }
To get the elements of set C, we will solve the quadratic equation
Solving x² −4x +3=0
x² −4x +3=0
x² -x −3x +3=0
x(x -1) -3 (x -1) = 0
(x -1)(x -3) = 0
x - 1 = 0 and x - 3 = 0
x = 1 and x = 3
∴ C = {1, 3}
- For (d) D = {x | x is the number of heads when six coins are tossed}
When six coins are tossed, it is possible to have
0 head, 1 head, 2 heads, 3 heads, 4 heads, 5 heads, or 6 heads
This implies x = 0, 1, 2, 3, 4, 5, and 6
∴ D = {0, 1, 2, 3, 4, 5, 6}
Among the sets above, we can observe that sets A and C are equal.
A = {1,3}
B = {x | x is a number on a die } = {1,3}
Hence, the events which are equal are (a) A = {1,3} and (c) C = {x | x2 −4x +3=0 }
Learn more on Equal sets here: https://brainly.com/question/24700823
