1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Maksim231197 [3]
3 years ago
11

Determine whether the statements in (a) and (b) are logically equivalent.

Mathematics
2 answers:
sertanlavr [38]3 years ago
8 0

Answer:

Not 100% but I think they are equal logically.

Andru [333]3 years ago
5 0

Answer:

The two statements are logically equivalent.

Step-by-step explanation:

Let X be the statement that Bob is a double math and computer science major.

Y be the statement that Ann is a maths major.

Z be the statement that Ann is a double maths and computer science major.

The two statements written in terms of X, Y and Z now

a. Bob is a double math and computer science major and Ann is a math major, but Ann is not a double math and computer science major.

(x and y) and not z

b. It is not the case that both Bob and Ann are double math and computer science majors, but it is the case that Ann is a math major and Bob is a double math and computer science major.

not (x and z) and (x and y)

Noting that for logical statements,

Negation is represented by ~

And is represented by conjunction sign Λ

Or is represented by disjunction sign V

(x and y) and not z

(x Λ y) Λ (~z)

not (x and z) and (x and y)

~(x Λ z) Λ (x Λ y)

We can then simplify the second statement to obtain the first statement and prove the equivalence of both sides

~(x Λ z) Λ (x Λ y)

Using DE MORGAN'S theory, ~(x Λ z) = (~x) V (~z)

~(x Λ z) Λ (x Λ y) = ((~x) V (~z)) Λ (x Λ y)

Then applying the distributive law to the expression, we can open the bracket up

((~x) V (~z)) Λ (x Λ y)

= ((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

Opening the first bracket up further

((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

= ((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

The NEGATION law shows that (~x Λ x) = c (where c is a negation law parameter for when two opposite statements are combined in this manner, it works like a 0 in operation)

((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

= (c Λ y) V ((~z) Λ (x Λ y))

But (c Λ y) = (y Λ c) = c (according to the UNIVERSALLY BOUND law, see how c works like a 0 now?)

(c Λ y) V ((~z) Λ (x Λ y))

= c V ((~z) Λ (x Λ y))

= ((~z) Λ (x Λ y)) V c (commutative)

And one of the foremost IDENTITY laws is that (any statement) V c = c

((~z) Λ (x Λ y)) V c

= ((~z) Λ (x Λ y))

= (x Λ y) Λ (~z)

Which is the same as the first statement!

PROVED!!!

Hope this Helps!!!

You might be interested in
Members of a lacrosse team raised $1396.75 to go to a tournament. They rented a bus for $850.50 and budgeted $28.75 per player f
4vir4ik [10]

Answer:

19 players

Step-by-step explanation:

If the team raises $1396.75 and the bus costed $850.50 then the remaining budget is = 546.75

If each meal is $28.75 then you could buy 19 meals for 19 players to take to the tournament.

7 0
3 years ago
10. The perimeter of a parallelogram is 72 meters. The width of the
nalin [4]

Answer:

Length is 20 meters and Width is 16 meters

Step-by-step explanation:

A parallelogram is a 4-sided figure with 2 pair of parallel sides.

The perimeter is the sum of all 4 sides of the parallelogram.

Let the length of parallelogram be x and width be y.

The perimeter is 72, thus we can write:

x + x + y + y = 72

or

2x + 2y = 72

Also, width is 4 less than length, thus we can write:

y = x - 4

Now, we replace the 1st equation with the 2nd equation and solve for x first. Shown below:

2x + 2y = 72

2x + 2(x - 4) = 72

2x + 2x - 8 = 72

4x = 72 + 8

4x = 80

x = 80/4 = 20

And now y:

y = x - 4

y = 20 - 4

y = 16

Thus, the Length is 20 meters and Width is 16 meters

4 0
3 years ago
HURRYYYYY UPPPP
Reika [66]

Kenneth wrote per page is 4

8 0
3 years ago
Helppp I don’t know what to doo
astra-53 [7]

Answer:

32

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 = 32

Times 2 by 2, 5 times. I don't know if that makes since.

7 0
3 years ago
Deborah has 104 baseball cards. She gave 16 baseball cards to her brother Corey. Then she put the remaining baseball cards in an
harkovskaia [24]

Answer:

10

Step-by-step explanation:

the answer is 9.77777777778 so round because you are not going to cut a page and you get 10.Hope this helps!

6 0
3 years ago
Read 2 more answers
Other questions:
  • Which rigid motion would map triangle ABC onto triangle A'B'C'?
    14·2 answers
  • What is (-5) to the -2 power simplified
    7·1 answer
  • A system of equations is graphed on the coordinate plane.
    8·1 answer
  • What is the Axis of Symmetry?
    15·1 answer
  • Math question can you answer it
    12·1 answer
  • Which one is it.<br>You can choose more than one.​
    5·2 answers
  • The diagonal AC is drawn in parallelogram ABCD Which method can NOT be used to prove that AABC is congruent to ACDA?
    9·1 answer
  • Can someone please give me the answer
    9·1 answer
  • Help me please help please
    10·1 answer
  • Luna flew from Boston to Orlando with a stop in Atlanta to switch planes. The flight from Boston to Atlanta was 3 hours and 30 m
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!