For the given claim, complete parts (a) and (b) below. Claim: At least 36% of Internet users pay bills online. A recent survey of 400 Internet users indicated that 39% pay their bills online. a. Express the original claim in symbolic form.

Q: Prove the following using natural deduction. -А > (А > В) (A → C V D) → ((A → C') V (A → D))

A: Given ¬A→A→B      (1) We have to prove it is the tautology. Since X→Y=¬X+Y               (2) Apply…

Q: Write above five statements into Mathematical logic b) State and prove first De Morgan Law.

A:

Q: State the converse, contrapositive, and inverse of the following conditional statement: Learning…

A: Let the conditional statement is If P then Q, the converse of the statement is if Q then P. The…

Q: Please draw the circuit diagram that corresponds to the following logical statement: "p v (qA "r)

A: We use properties of logical circuit.

Q: Determine whether the following are tautology, contingency or contradictions. a.((~p ∧ q) ∧ (q ∧ r))…

A: The opposite of tautology is contradiction.  A contradictory statement is always false. If any truth…

Q: Validate the following argument form using inference laws. pVr -qVs pAq -(r-s)

A: F1 : ~p V r F2 : ~q V s F3 : p ∧ q      : p [F3a]   &   q [F3b] Goal, G : ~(r -> ~s)…

Q: Express the original claim in symbolic form. Claim: 60% of homes have smoke detectors. O A. H=0.6 O…

A: According to the given information, we have Claim: 60% of homes have smoke detectors.

Q: Are the following expressions logically equivalent? Could you help me create a truth table for it?…

A: Consider the given information.   Now make the true table for the given relation,

Q: Use rules of inference to prove if the assertation is valid, if not show why.

A: The given argument is not valid. See the proof below

Q: Express the original claim in symbolic form

A: Let p be the proportion of adults that would erase their personal information if they could. Claim:…

Q: The following premises are given. Choose the order of rules of inference that are listed below to…

A: The given premises are: ~p ~r ~p or q →r Find the order of rules inference to show that q must be…

Q: QUESTION 3 State whether or is being used in the exclusive or inclusive sense in the given…

A: Inclusive  allows both possibilities as well as either of them. So, if either A or B is True, or if…

Q: Prove the following using natural deduction. (b) -А — (А > В)

A: We prove this by using rules of inference.

Q: State whether or is being used in the exclusive or inclusive sense in the given statement. The prize…

A: Inclusive OR allows both possibilities as well as either of them. So, if either A or B is True, or…

Q: A nondirectional assertion would involve what kind of test?

A: Non-directional assertion

Q: What rule of inference starts with an implication? A simplification B disjunctive syllogism Cmodus…

A: Given:   Rule of interface start with Implication

Q: What type of error, if any, occurs in the following deduction? All fishes breathe in water to live…

A: The error occurred here is assumption error.

Q: Is PA (QV R) logically equivalent to (P^Q) v (PAR)? O yes no

A:

Q: For the given claim, complete parts (a) and (b) below. Claim: At least 26% of Internet users pay…

A:

Q: In the following, prove some alternative rules of inference. a) Strengthening  { (P → Q ) } ⊢ ((P…

A: 1. P→Q                                      A 2. P∧R                                       A 3. R→Q…

Q: Is the following a valid deduction: P-QAQ-R .. R Yes No

A: Given that the deduction is,

Q: Construct a formal proof of validity of the argument. ~p (~pv~o) → ~(~ n) ~ m → (o → ~ n) m → ~n ::…

A:

Q: In formal symbolic logic, show that [P&∼P]⊃Q is a theorem.

A: This is a problem of Logic.

Q: The following arguments are valid. Give a formal deduction for each. a. Premises: A → (BC), (C →…

A: What is Natural Deduction: Natural deduction is a type of proof calculus used in logic and proof…

Q: What is the logical equivalent to the implication P→ Q O PV Q OPAQ O ¬QVP O ¬P v Q

A:

Q: Use the 8 inference rules to prove the following arguments. a) ~P (Q v P) - R P v S…

A:

Q: No electric-powered car is a polluter. into symbolic form

A: “No electric-powered car is a polluter.”

Q: 2. Construct a formal proof of validity by adding statements to the given premises using rules of…

A: 2 A. Given,           1.      p∧q→r          2.    p/∴q ∧r¯

Q: Determine whether the following statement forms are logically equivalent: Attachment

A: Given statements are,

Q: Which of the following statements is supported by the bar chart?

A: Positive association: The two variables are said to be positively associated when values of one…

Q: Which statement-the converse, the inverse, or the contrapositive-always has the same truth or…

A: Solution: Let's define the terminology converse, inverse, and contrapositive statements  Converse…

Q: State the rule of inference by which its conclusion follows from its premise or premises. ~ (B · C)…

A: Introduction: There are some rules of interference: Modus Poneus: a⊃ba∴b Modus Tollen: a⊃b~b∴~a…

Q: 6. Determine whether PA ((¬P) V (¬Q))) is a tautology, contradiction, or neither.

A:

Q: a) Identify the claim and state Ho and H,. What is the claim? O A. Exactly 39% of all adults think…

A: (a) The claim of the test is at least 44% of adults in a certain country think the government is not…

Q: Use the 18 rules of inference to derive the conclusions of the following symbolized arguments. A.…

A: Answer for sub question 1: Since, S∧K→R, by conditional disjunction it follows that ¬S∧K∨R holds…

Q: State the rule of inference by which its conclusion follows from its premise or premises. (CVD) ɔ…

A:

Q: Determine whether the following argument is valid or invalid using a truth table. Justify your…

A: prem1:q-> r∧p prem1:p⊕r Conclusion:p∨q

Q: The records of a computer retail store show that out of the S0 customers who purchased a desktop…

A: Given that out of 50 desktop customers, 39 purchased service plan. Out of 20 notebook customers, 19…

Q: QUESTION 16 What is the major term in the following syllogism? "All first-degree murders involve…

A: The predicate of the conclusion is called Major Term. Thus (a) First degree murder is the Major…

Q: Determine if the following is a valid deduction rule: P (QV R) -(P → Q)

A: To determine if the following is a valid deduction rule:

Q: State, with brief reasons, whether q a [(P v q) → ] is a tautology, contradiction, or neither. a

A:

Q: 20% of adults smoke. Express the original claim and symbolic form.

A: Solution: Let p be the population proportion of adults who smoke.

Q: Determine the following ; Conclusion HYPOTHESIS Calculation

A: The t test are used to compare the mean significance between the two sample. It is used when the…

Q: Write the contrapositive statement for the following conditional statement: If the llama is black,…

A:

Q: C. Define a tautology, a contradiction and a contingency.

A: We have to define Tautology, Contradiction and Contingency with examples as follows.

Q: Construct the formal proof of validity for each of the following arguments.

A:

Q: State the rule of inference by which its conclusion follows from its premise or premises. (A ɔ B) ɔ…

A:

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.