4) Determine the validity of each argument. a) If Mary is wearing green socks, she has passed algebra. But Mary is wearing blue socks. Unfortunately, she must have failed algebra. b) Determine whether the argument is valid. If 8 is even, then 4 does not divide 5. Either 7 is not prime or 4 divides 5. But 7 is prime. Therefore 8 is odd (not even).

Choose all the answers below that are impossible. There may be zero, one, or more impossible answers. (Don't choose possible answers). An invalid argument that has true premises and a false conclusion. A valid argument that has true premises and a false conclusion. A valid argument that has false premises and a false conclusioon. A knight or knave who says "I am a knave". A knight or knave who says "My brother and I are both knaves".

PLEASE ANWER D, E, & FThe square of an irrational number is irrational.(a) Write the statement more formally, using quantification symbols (∀, ∃).(b) Write an informal negation of the statement. Be sure to avoid negations that are ambiguous.(c) Write a more formal negation of the statement, using quantification symbols (∀, ∃).(d) Is the original statement true or false? If true, explain. If false, give a specific counterexample.(e) Write an informal converse of the original statement.(f) Write a more formal converse of the original statement, using quantification symbols (∀, ∃).(g) Write an informal contrapositive of the converse of the original statement (i.e., a contrapositive of your statement in part (e)).(h) Write a more formal contrapositive of the converse of the original statement, using quantification symbols (∀, ∃). (i) Is the converse of the original statement true or false? If true, explain. If false, give a specific counterexample.

Answer these questions, Write it with pencil and show how you solved it A. Write the following statement in its contrapositive, converse, and inverse forms. If x is nonnegative, then x is positive or x is 0.   B. Write negations for the following statements If P is a square, then P is a rectangle.

Classify and explain (in at most 3 sentences) why each argument is deductive orinductive. Write D if it is a deductive argument and I if it is an inductive argument.A. 1. My television set did not work two nights ago.2. My television set did not work last night.Therefore, my television set is broken.B. 1. All electronic devices give their owners grief.2. My television set is an electronic device.Therefore, my television set gives me grief.C.1. I ate a chili dog at Joe’s and got indigestion.2. I ate a chili dog at Ruby’s and got indigestion.Therefore, chili dogs give me indigestion.D.1. All spicy foods give me indigestion.2. Chili dogs are spicy food.Therefore, chili dogs give me indigestion.E. The population of Tarlac City has risen steadily for the past 30 years. It is logicalto predict that the population of Tarlac City will rise next year.

Give five (5) equivalent statements and give its contrapositive, inverse, and converse statements. a. No insect is useless.

Michelle draws a restangle with a length of 6 cm. She draws a second rectangle with a length of 11 cm. Belinda continues drawing more rectangles, where for each restangle drawn, she uses a length that is 5 more centimeters than the length of the previous rectangle. If this pattern continues, what will be the length of the 11th rectangle?

Answer this question and show how you've solved it Rewrite the statement in if-then form in two ways, one of which is the contrapositive of the other. Being divisible by 3 is a necessary condition for this number to be divisible by 9.

Please help.

Consider the following statement. v integer n, if n is divisible by 6, then n is divisible by 2 and n is divisible by 3. Which of the following is a negation for the statement? O v integer n, if n is divisible by 6, then n is not divisible by 2 or n is not divisible by 3. O3 an integer n such that n is divisible by 6 and either n is not divisible by 2 or n is not divisible by 3. O3 an integer n such that n is not divisible by 6 and either n is not divisible by 2 or n is not divisible by 3. O3 an integer n such that n is not divisible by 6 and n is divisible by 2 and n is divisible by 3. Ov integer n, if n is divisible by 2 and n is divisible by 3, then n is not divisible by 6.