1.Logical equivalence of two English statements. Define the following propositions: j: Sally got the job. l:...

1.Logical equivalence of two English statements.

Define the following propositions:

j: Sally got the job.
l: Sally was late for her interview
r: Sally updated her resume.

Express each pair of sentences using a logical expression. Then prove whether the two expressions are logically equivalent.

(a)

If Sally did not get the job, then she was late for interview or did not update her resume.
If Sally updated her resume and was not late for her interview, then she got the job.

(b)

If Sally got the job then she was not late for her interview.
If Sally did not get the job, then she was late for her interview.

(c)

If Sally updated her resume or she was not late for her interview, then she got the job.
If Sally got the job, then she updated her resume and was not late for her interview.

can you please provide a truth table for each?

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

3. For each of the English statements below, do the following: i. Define propositions as necessary,...

3. For each of the English statements below, do the following: i. Define propositions as necessary, ii. Write the symbolic notation for the implication, iii. Write the symbolic notation for the inverse then write in English, iiii. Write the symbolic notation for the contrapositive then write in English. Note: The sentences should be written in a form consistent with the original sentence. So for instance if the original sentence begins with ‘It is necessary’ the other sentences should begin with...

Explain the logical structure of the following set of propositions - a theory. 1.The set of...

Explain the logical structure of the following set of propositions - a theory. 1.The set of languages accepted (decided) by deterministic Turing machines = the set of languages accepted (decided) by nondeterministic Turing machines 2. PATH belongs to P 3. TAUTOLOGY is a member of coNP 4. 2 definitions for NP (1 in terms of a polynomial verifier 2 in terms of a nTM) are equivalent 5. PSPACE = NPSPACE 6. NP is a subset of PSPACE 7. SAT belongs...

Write two simple logical statements in English. Negate your second simple statement. Then write out a...

Write two simple logical statements in English. Negate your second simple statement. Then write out a compound statement using your first simple statement and the negated statement with the following connectives. In each case evaluate the truth value of your compound statement. (a) Logical AND (b) Logical OR (c) Logical XOR (d) Logical implication

Consider the following data for two risk factors (1 and 2) and two securities (J and...

Consider the following data for two risk factors (1 and 2) and two securities (J and L): λ0 = 0.06 bJ1 = 0.75 λ1 = 0.03 bJ2 = 1.30 λ2 = 0.04 bL1 = 1.60 bL2 = 2.10 Compute the expected returns for both securities. Round your answers to two decimal places. Expected return for security J: % Expected return for security L: % Suppose that Security J is currently priced at $21.00 while the price of Security L is $12.25. Further,...

What is Russell L. Ackoff trying to say in the two statements below? 1.)"improving the performance...

What is Russell L. Ackoff trying to say in the two statements below? 1.)"improving the performance of the parts of a system taken separately will not necessarily improve the performance of the whole.” 2.) “Systems thinking is holistic, it attempts to derive an understanding of the parts from the behavior and properties of wholes rather than derive the behavior and properties of wholes from those of their parts.”

1) Define the following: Standardization, titrant, primary standard, acid/base indicators, indicator range, end point, equivalence point,...

1) Define the following: Standardization, titrant, primary standard, acid/base indicators, indicator range, end point, equivalence point, titration curve, buffer solution.   2) What are the requirements for a primary standard?   3) Write the transition range and color change for the following indicators: Phenolphthalein,  bromocresol green, methyl orange.   5) What is the aim of standardization?   6) What is the difference between primary standard and standard solution?   7) Define and compare end-point and equivalence point.   8) Why the weak acids cannot be used...

1. For each of the following statements, define all of the underlined terms. Then, explain why...

1. For each of the following statements, define all of the underlined terms. Then, explain why the statement is true, false or uncertain. (a) If a consumer views two goods as perfect substitutes then their optimal choice will be a corner solution. (b) The substitution effect from a price increase states that the consumer will always choose a smaller amount of that good to consume. However, the income effect states that consumption can move in either direction. (c) Suppose Alf...

(a) Consider the following two stage process: Stage 1. The system absorbs 83 J of...

(a) Consider the following two stage process: Stage 1. The system absorbs 83 J of heat and during this process it had 44 J of work done on it. Stage 2. The system absorbs 63 J of heat and during this process it does 27 J of work on the surroundings. Calculate Q, w, and ΔE for the overall process (b) A piston is compressed from a volume of 7.5 L to 2.2 L at a constant...

Discuss the following two statements: 1- the corporate charter and the bylaws of a company are...

Discuss the following two statements: 1- the corporate charter and the bylaws of a company are legal documents; therefore, they should not be examined by the auditors. If the auditor wants information about these documents, an attorney should be consulted. 2- the most important audit procedure to verify dividends for the year is a comparison of a random sample of cancelled dividends checks with a dividend list that has been prepared by management as of the dividend record date.

Discuss the following two statements: (1) If we have an unobserved variable in an equation and...

Discuss the following two statements: (1) If we have an unobserved variable in an equation and we are interested in the sign of its coefficient, we should always use a proxy, since the estimated coefficient of the proxy will give us the correct sign. (2) In regressions of income (or wage) on schooling where schooling is measured with error, omitting variables that measure ability will overestimate the effect of schooling on income.

Subjects