1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MAXImum [283]
3 years ago
5

For each of the following, use logic laws to decide whether the statement is a tautology contradiction, or neither. a (a) (A B)

A (B A) (b) (PP) AP

Mathematics
1 answer:
spayn [35]3 years ago
8 0

Answer:

The statement (A\rightarrow \lnot B)\land (B\rightarrow A) is a contingency.

The statement (P\rightarrow \lnot P)\land P is a contradiction.

Step-by-step explanation:

A tautology is a proposition that is always true.

A contradiction is a proposition that is always false.

A contingency is a proposition that is neither a tautology nor a contradiction.

a) To classify the statement (A\rightarrow \lnot B)\land (B\rightarrow A), you need to use the logic laws as follows:

(A\rightarrow \lnot B)\land (B\rightarrow A) \equiv

\equiv (\lnot A \lor\lnot B)\land(\lnot B \lor A) by the logical equivalence involving conditional statement.

\equiv (\lnot B\lor \lnot A )\land(\lnot B \lor A) by the Commutative law.

\equiv \lnot B \lor (\lnot A \land A) by Distributive law.

\equiv \lnot B \lor (A \land \lnot A) by the Commutative law.

\equiv \lnot B \lor F by the Negation law.

Therefore the statement (A\rightarrow \lnot B)\land (B\rightarrow A) is a contingency.

b) To classify the statement (P\rightarrow \lnot P)\land P, you need to use the logic laws as follows:

(P\rightarrow \lnot P)\land P \equiv

\equiv (\lnot P \lor \lnot P)\land P by the logical equivalence involving conditional statement.

\equiv P \land (\lnot P \lor \lnot P) by the Commutative law.

\equiv (P \land \lnot P) \lor (P \land \lnot P) by Distributive law.

\equiv F \lor F \equiv F by the Negation law.

Therefore the statement (P\rightarrow \lnot P)\land P is a contradiction.

You might be interested in
The mean is 0.500 and the standard deviation is 1.84 x 10-3. Gaussian Statistics Apply. How many replicate determinations are ne
Dmitriy789 [7]

Answer:

I don't know but do you know how to answer this:

Two similar right triangles have areas of 6 square inches and

150 square inches. The length of the hypotenuse of the smaller

triangle is 5 inches. What is the sum of the lengths of the legs

of the larger triangle?  

7 0
3 years ago
Read 2 more answers
The set of numbers that includes the whole numbers and their opposites is called the set of...?
Nookie1986 [14]

Step-by-step explanation:

option C is the answer

hope it helps

7 0
1 year ago
What is the answer??<br>12=√160-r
babunello [35]
The answer is r=16 you have to square everything

6 0
2 years ago
Read 2 more answers
If I equals PRT which equation is equivalent to T
snow_lady [41]
I = P · R · T
Divide both sides by P·R
I/(P·R) = T

Answer: \frac{I}{PR} = T
7 0
3 years ago
which property does the example shows. 23.1+42.6=42.6+23.1. A. associative property of addition or B.Distributive property
konstantin123 [22]
A) distributive is where it distributes a number through a set of parenthesis.
4 0
3 years ago
Read 2 more answers
Other questions:
  • Richelle drew a hexagon KLMNOP at the right. She thinks the hexagon has six congruent angles. How can she show that the angles a
    14·1 answer
  • Consider the polynomial 16x2 – 1. What is the value of ac? What is the value of b? What two numbers multiply to get ac and add t
    11·2 answers
  • Twenty-four blue socks and twenty-four red socks are lying in a drawer in a dark room. What is the minimum number of socks you n
    8·1 answer
  • A theater company charges $3.50 per ticket for people of all age groups. If c represents the total number of children who bought
    14·1 answer
  • Find the general form, Ax2+Ay2+Dx+Ey+F=0, by identifying the coefficients A,D,E,&amp;F center:(0,1); r=1 (x-0)2+(y-1)2=1 x2+y2-2
    9·2 answers
  • M= 2n - 2 <br> solve for n
    8·1 answer
  • A 12 oz soda costs $1.25 in the vending machine. At that rate, how much would a<br> 48 oz soda cost?
    14·1 answer
  • Suppose we want to choose five objects without replacement from 14 distinct objects if the order of the choices is taken into co
    14·1 answer
  • Ms. Griffith took a cab ride which cost $16. She gave the driver $20 and said, "keep the change." What percent did Ms. Griffith
    11·1 answer
  • Correctly write 36.2 x 103 in scientific notation.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!