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
I am Lyosha [343]
3 years ago
7

The symbol ⊕ is used to denote exclusive or, so p ⊕ q ≡ (p v q) ^ ~ (p ^ q).

Mathematics
1 answer:
Elan Coil [88]3 years ago
3 0

I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.

⊕ = XOR

∨ = OR

∧ = AND

~ = NOT

↔ = IFF (meaning "if and only if")

→ = IMP (short for "implies")

and for logical equivalence I'll use a regular equal sign.

Then

p XOR q = (p OR q) AND NOT (p AND q)

(a) By definition of XOR, we have

p XOR p = (p OR p) AND NOT (p AND p)

= p AND NOT p

and this is tautologically FALSE.

(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:

NOT (p AND q) = NOT p OR NOT q

Then we can interchange the AND and ORs using their respective distributive properties. That is,

p XOR q = (p OR q) AND (NOT p OR NOT q)

= (p AND (NOT p OR NOT q)) OR (q AND (NOT p OR NOT q))

= ((p AND NOT p) OR (p AND NOT q)) OR ((q AND NOT p) OR (q AND NOT q))

Both (p AND NOT p) and (q AND NOT q) are tautologically FALSE, so the truth value of either OR depends only on the other statements, so we have

p XOR q = (p AND NOT q) OR (q AND NOT p)

Recall the definition of IFF:

p IFF q = (p IMP q) AND (q IMP p)

Also recall that IMP is logically equivalent to

p IMP q = p OR NOT q

Then we have

p IFF q = (p OR NOT q) AND (q OR NOT p)

so that its negation is

NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))

= NOT (p OR NOT q) OR NOT (q OR NOT p)

= (NOT p AND q) OR (NOT q AND p)

The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).

You might be interested in
What is the beat values of averages, such as mean, median, and mode, are known as
IrinaVladis [17]
A) Standard deviation
3 0
3 years ago
Solve the following equation. Then place the correct number in the box provided.
Greeley [361]

3x+1=2x+12

3x-2x=12-1

x=11

6 0
3 years ago
Read 2 more answers
Find the value of 9x + 2 given that -5x-3=2​
Sloan [31]

-5x-3 = 2\\-5x=5\\x = -1

Now plug the x value into 9x + 2

9(-1)+2) = -7

Hope that helps!

7 0
3 years ago
Which statement about the two triangles is correct
Bess [88]

Answer:

They might be the same type of triangle

Step-by-step explanation:

8 0
3 years ago
Hey, can someone please explain how to do this
Natasha2012 [34]

Answer:

i am learning this right now and i think that all you would have to do is the number into the "equation" with the negative sin, cos, tan, close the parenthesis then press enter or =

Step-by-step explanation:

Sin^-1(-45)=

cos^-1(-45)=

tan^-1(-45)=

4 0
3 years ago
Other questions:
  • Write the following decimal number in its equivalent fraction form. Show all work for full credit.
    5·1 answer
  • A rectangular rug is 4 feet by 9 feet. What is the side length of a square with the same area.
    5·2 answers
  • Please help! brainliest, rattings, thanks ect, the attachment is posted below
    15·1 answer
  • Answer 16., 17., and 18., Text me after you have..!
    10·1 answer
  • For what value of x does 64^3x = 512^2x+12
    5·1 answer
  • 100% with 8 equal parts
    15·1 answer
  • 2 positive integers have hcf of 12 and their product as 6336 number of pairs possible for the number is​
    9·1 answer
  • Entos,
    6·1 answer
  • This is your question please help me ​
    5·1 answer
  • The second part of the problem is where i need help. The answers i have there have been given by other tutors
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!