A)
P | Q | (PQ) | P(PQ) |
---|---|---|---|
T | T | T | T |
T | F | T | T |
F | T | T | T |
F | F | F | T |
So,it is a tautology.
B)
A | B | (AB) | (AB) | (AB)(AB) |
---|---|---|---|---|
T | T | T | T | T |
T | F | F | F | T |
F | T | F | T | T |
F | F | T | T | T |
So,it is a tautology.
C)
P | (~~P) | P(~~P) |
---|---|---|
T | T | T |
F | F | T |
So,it is a tautology.
D)
P | Q | (~P~Q) | (QP) | (~P~Q)(QP) |
---|---|---|---|---|
T | T | T | T | T |
T | F | T | T | T |
F | T | F | F | T |
F | F | T | T | T |
So,it is a tautology.
Therefore, HENCE PROVED.
ngument, and mat he pages are stapled together. Question 1- Provide a proof that demonstrates the...
Part 3 (one point total). For each of the following sequents, provide a proof that demonstrates their validity. Make sure to use SL and the primitive rules (no derived rules). 1. AB,BC FAC 2. A->B, BC, DEA&D-E&C 3. -AVB, -BVC, -DVEA&DE&C 4. -AVB, -DVEF (A-B)&(D–>E) 5. ( AB)+((B+C)&( DE), A +-AVBA&D>E&B 6. P→Q-QT-P 7. P Q –QF -P 8. P Q -PF-Q 9. P&PTD 10. P-Q, Q--PF P™D
point. Multiple pages must be stapled together, a stapler is available at the collecti boxes Answer all questions. Question 1-5 points The figure below shows a point charge and two of its associated equipotential lines which have radii of 2 cm and 4 cm respectively. (a) Calculate the electric potential at points A, B and C. (b) Calculate the electrie potential energy of an electron placed at each of these points. +3nC (c) Calculate the potential difference AVAB and ΔVBC...
pages 1-4 go together, and last question is separate but needs an answer. separate question: Which state of matter is the most energetic? give a reason for your answer. CHEM&121 WS-11: Equilibrium Worksheet 1. Write the equilibrium expression for the following reactions: a. 200+ 0 2CO b. COCl2 CO + Cl2 c. CS2 + 4H CH. +2H:S d. 2SO2 + 0 2SO e. 2C1:05 O2 + 4CIO 1 2. A sample of gaseous BrCl is allowed to decompose in a...
Provide an ? N proof to prove that the following sequences converge. Question (e), please. 5. Provide an e – N proof to prove that the following sequences converge. (a) {ne cos(n)} (b) {zo Bom} (c) {(-1)In (n)} (d) an = 2 + 1 (@) an = V1 -
Match the following: item 1. Indirect proof which assumes the opposite of a statement and shows this creates a logical inconsistency item 2, Indirect proof applied to a statement of the form P→Q which instead proves-Q→-P. item 3. Proves a "there exists" statement by finding a specific element for which the statement is true item 4. Disproves a "for all" statement by finding a specific element for which the statement is false. item 5. Proof where a statement is split...
1. Please provide a natural deduction proof for the following valid, deductive argument: Premise 1: ~ ( F & A ) Premise 2: ~ ( L v ~ A ) Premise 3: D > ( F v L ) / ~ D 2. Answer the following question: can one prove invalidity with the natural deduction proof method? Why or why not? 3. Answer the following question: can one construct a natural deduction proof for an invalid argument in SL? Why...
1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an= n-cos(n) 4n2-7 Tn (d) { } 2. Prove that the following sequences diverge. (Def 7.10 pg 596) READ Sequences that Diverge to oo or-oo (b) ann infinity. Hint: Provide an M -N proof that an approaches 1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an=...
For each case specify the state of the substance and provide the requested values. A) (8 points) Refrigerant 134a at T 10 C and v 0.025 m/kg, find P in kPa and u in B) (7 points) Air at P-1 bar and v-1 m3/kg, find u in kJ/kg. C) (8 points) Water at T 820 C and P 0.35 MPa, find h in kJ/kg. D) (7 points) Refrigerant 134a at T=4°C and u = 55.1 kJ/kg, find v in m3/kg....
provide structures for the spectral data provided Pages 1-5: provide the 5 structures for the spectral data provided. For full credit, you must be sure to assign/label all the NMR peaks and assign the major IR bands including those readily identifiable in the fingerprint region (use the IR spectral tables handed out in class). If you do not label anything on the spectra, you will lose most of the points for this problem set. Hint for the problems listed without...
Question 7 Classify each of the following sets as finite, countable infinite, or uncountable (no proof is necessary): A=0 B = {2 ER: 0 < x < 0.0001} C=0 D=N E = {R} F= {n EN:n <9000} G=Z/5Z H = P(N) I= {n €Z:n > 50 J=Z Bonus: Give an example of a set with larger cardinality then any of the above sets.