# laws

1. ### HELP!! : Discrete Math ; boolean / Algebra Proposition (Laws)

Here's the given problem.. p AND (q OR r) IMPLIES (r OR (q OR p)) = p OR q ( = meaning equivalent) So I have already solved my truth table for this problem, Now I have to write them down step by step and prove that: p AND (q OR r) IMPLIES (r OR (q OR p)) is equivalent to p OR q by using...
2. ### Limit laws not working?

Hi everyone, I tried to apply the limit laws here & use substitution to come to the answer that the limit of x->a f(x) = 3/2 and the lim of x->a g(x) = 1/2 therefore the product & answer = 3/4. the textbook says the answer is -5 though.. Anyone know what I have assumed falsely etc how to...
3. ### Prove using these laws without truth tables?

Can someone explain to me in detail how to complete these two problems without using truth tables? I'm having a hard time understanding what to do. I know that I'm supposed to use the laws, etc. But I'm confused on this entirely. Prove that ((p → q) ∧ ¬q) → ¬p is a tautology without...
4. ### monotonic laws for ordinal subtraction

I have to prove some monotonic laws for ordinals. It's quite comfortable for me to show monotonic laws of ordinal addition (e.g. $\beta\leq\gamma\Rightarrow\alpha+\beta\leq\alpha+\gamma$). But when it comes to laws with subtraction, then I'm not sure where to start. Maybe it's because of...
5. ### Using logic laws

Hi , honestly I tried every way to begin solving this issue but I didn't even where to start ....please please help me do it . note : the questions is attached I could do it using truth table but it's not what is required thank you
6. ### De Morgan's Laws

Does my venn diagrams represent De Morgan's laws correctly?

2(3mn4)3 ​=
8. ### Problem having to do with limit laws

"Let If is a function which is continuous everywhere, then we must have m=" I don't remember how I did this problem, only that I did it wrong... Please help.
9. ### Prove using rules of inference and logic laws

(B-->R) and (BL -->Y) and (BL --> ~R) --> (B--> Y) 1. (B-->R) - hypothesis 2.(BL -->Y) - hypothesis 3. (BL --> ~R) - hypothesis how do i arrive at (B--> Y)?
10. ### laws of propositional logic to simplify

simplify the following using laws of propositional logic: ~[p --> ~(p ^ q)]
11. ### Laws of Exponents dealing with fractions

I have a problem to solve but I am stuck trying to find out how to determine the correct answer. If it was the same variable I would be able to do it but since it's two variables (m and n) I'm not sure how to proceed. I am supposed to re-write it as a single exponent. Please forgive me if the...
12. ### Exponent laws!

Is anyone having trouble with negative exponents or exponent laws in general? If you are, reply so I could try my best to help you out!
13. ### Find the Missing parst of the Triangle Using the Laws of Cosines

Hey people. Here's the question. Find the missing parts of the triangle by using the laws of cosines. What's known is, B=27, a=11, c=22 Solving for b, b^2=11^2+22^2-2(11)(22)(cosB) b^2=121+484-2(242)(.891) b^2=605-432 b^2=\sqrt{173} b=13.2 Solving for A...
14. ### Boolean Laws, and Theorem

What's up wonder community of math wizards. I was hoping you could check a problem for me. For every step I need to pick which numbered law from the list was used. HERE IS THE LIST. Given =\overline{(A\overline{BC}+\overline{AC})(\overline{A+B)}} 19...
15. ### Laws of Exponents

I have a question from a book I am reading but I am guessing I do not understand it since it makes no sense to me. I understand exponents just fine but I am guessing this is more of a proof question, which I am not so good at. Prove the given Laws of Exponents for the case in which m and n are...
16. ### Applying the Laws of Sines or Cosines

Solve the triangle. A = 19°, C = 102°, c = 6 choices are B = 31°, a ≈ 18, b ≈ 15.8 B = 59°, a ≈ 2, b ≈ 5.3 B = 59°, a ≈ 18, b ≈ 15.8 B = 59°, a ≈ 18, b ≈ 5.3
17. ### Applying the Laws of Sines or Cosines

Solve the triangle. B = 36°, a = 41, c = 17 choices are b ≈ 29, C ≈ 20, A ≈ 124 b ≈ 44, C ≈ 20, A ≈ 124 b ≈ 29, C ≈ 121, A ≈ 23 b ≈ 44, C ≈ 24, A ≈ 120
18. ### Using index laws to simplify this equation

Could anyone help me simplify this equation using index laws:
19. ### Exponents+Fractions

(-8/5)7/4 x (-8/5)1/4 -3a-3b-7c-6/12a-6b-3c-3 n-2n6 x m3n-8 (64a12b15)2/3
20. ### Exponent Laws

I need help with these 2 questions :