Answer the following questions. Explain your reasoning:
a) Without using the truth table, prove if the following statement is tautology
or not.
((r→q) ⋁ ((q∧r)→q)) ∧ (r→(s→r))
[2 marks]
b) Without using the truth table, show that the following statements are true:
i.
P(q v r) ≡ (p ∧ ¬ q)  r
ii.
(¬p → q) ∨ (r → q) ≡ r → (p ∨ q)
c) Rewrite each sentence symbolically:
i.
ii.
The product of any two real numbers x and y is negative.
There are real numbers x and y such that x+3= 4y.
[4 marks]
[2 marks]
[2 marks]
d) For the following statement, write down a logically equivalent statement
which contains no operators other than ¬ and ∧:
�
� ∨(→)

Question

06-07-2024
Mathematics

Answered

IDNLearn.com is designed to help you find the answers you need quickly and easily. Ask anything and receive prompt, well-informed answers from our community of experienced experts.

Answer the following questions. Explain your reasoning:
a) Without using the truth table, prove if the following statement is tautology
or not.
((r→q) ⋁ ((q∧r)→q)) ∧ (r→(s→r))
[2 marks]
b) Without using the truth table, show that the following statements are true:
i.
P(q v r) ≡ (p ∧ ¬ q)  r
ii.
(¬p → q) ∨ (r → q) ≡ r → (p ∨ q)
c) Rewrite each sentence symbolically:
i.
ii.
The product of any two real numbers x and y is negative.
There are real numbers x and y such that x+3= 4y.
[4 marks]
[2 marks]
[2 marks]
d) For the following statement, write down a logically equivalent statement
which contains no operators other than ¬ and ∧:
�
� ∨(→)

Sagot :

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.

Write The Equilibrium Expression For The Following Reaction:[tex]\[ Cd_{(aq)}^{2+} + 4 Br_{(aq)}^{-} \longleftrightarrow CdBr_{4(aq)}^{2-} \][/tex]A. [tex]\[ K=

Unit Test ReviewWhich Statement Describes Mustafa Kemal?A. He Served As The Last Shah Of Iran.B. He Became The First President Of Turkey.C. He Helped Found The

This Is Part Of A Bus Timetable Between Birmingham And Coventry.\begin{tabular}{|l|l|l|l|l|l|l|}\hline Birmingham & 0705 & 0733 & 0808 & 0838 &a

9. The Explosion Of Free Trade And International Business Activity In The Early 20th Century Would Not Have Been Possible Without The Willingness Of Most Major

Complete The Table Below.John Honest Created The Following Table To Determine The Asset Value Per Share And The Number Of Shares Purchased (to The Nearest Tenth

Which Of The Following Was NOT An Achievement Of The Women's Health Movement?A. Gender-based Research Emerged.B. Women Gained More Control Over Their Reproducti

A White Solid Disappears When It Is Stirred Into Water. It Does Not Have A Bright Or Reflective Luster. Which Of These Properties Does The Substance Demonstrate

Match The Three Suffixes To Their Definitions.\begin{tabular}{l|l}Suffix & Definition \\\hline-able; -ible & A) Is, Can Be \\\hline-less; -ant & B)

Were The Actions Of The Spanish Any More Cruel And Reprehensible Than Those That The Native Leaders (such As The Aztec Chiefs And Priests) Inflicted Upon Their

Which Object Was Once Considered A Planet, But Is Now Classified As A Dwarf Planet Because Of Its Size?A. MercuryB. PlutoC. JupiterD. Mars

Sagot :

Other Questions