Mapa Institute of Technology - GED 102

1)For real numbers x and y, define x y = 1 + x + y

 

What would be the inverse of 5 with the respect to this operation?

 

 

 

 

 

 

Q2: Find a point on AB such that AB is divided into segments that form the Golden Ratio. If the length of the line segment is 7 cm, then what is the distance of the point from A to form a Golden Ratio?

 

 

 

 

 

Q3: Benoit Mandelbrot is best known for his work on

 

 

 

 

 

 

Q4: Determine the 23rd Fibonacci number if the 22nd Fibonacci number is 17711 and the 24th Fibonacci number is 46368

 

 

 

 

 

Q5: According to Stewart (Nature's Numbers), Mathematics is a formal system of thought for   ,

       , and        patterns.

 

 

 

 

 

Q6: For real numbers x and y, define x * y = 1 + x + y. This binary operation is

 

1. Commutative

 

2. Associative

 

 

 

 

 

Q7: In the argument " not P -> (Q or not R and S)" which symbol is the "major connective" (the one from which the validity is based)?

 

 

 

 

 

Q8: Consider a propositional language where P: x is a prime number.

Q: x is odd.

 

 

 

Which of the following is equivalent to the implication P -> Q?

 

 

 

1. x being prime is a sufficient condition for x being odd.

 

2. x being prime is a necessary condition for x being odd.

 

3. x being odd is a necessary condition for x being prime.

 

4. x being odd is a sufficient condition for x being prime.

 

 

 

 

 

 

Q9: For real numbers x and y, define x * y = 3x + y. Evaluate 8 * 3

 

 

 

 

Q10: In the mathematical sentence 4x + 5 = 15, which is the pronoun?

 

 

 

 

 

 

Q11: The proposition "Kara does not submit the requirement or she fails the course" is what type of proposition?

 

1. Disjunction

 

2. Conditional

 

 

 

 

 

 

Q12: The quantifiers that are used to denote that all elements in the set satisfy the given property are referred to as

 

 

 

 

 

Q13: In the statement A = {2, 4, 6, 8}, which is the subject?

 

 

 

 

 

 

 

14. The 30th Fibonacci number with two initial values both equal to 1 is _______

 

 

15. Let Fib(n) denotes the nth Fibonacci number with two initial values both equal to 1. Find the sum Fib(2)+Fib(3)+Fib(4)+Fib(5).

 

 

 

 

 

 

 

16.NThe Golden Rectangle is a rectangle whose sides form the Golden Ratio. The ratio of the longer side to the shorter side in a rectangle form golden ratio. What is the approximate dimension of the longer side of the rectangle if the shorter side is 2.1 cm?

 

 

 

 

 

17. The number of leaves of a certain plant follows that of the Fibonacci sequence. If there is one leaf on the first day and two leaves on the second day, how many leaves does the plant have on the 15th day?

 

 

 

 

 

18. Write the negation of the statement "If you decide to go to the party, then I will go with you".

 

 

 

 

 

 

 

19. Let A be the statement "Kara is Asian" and B be the statement "Mia is American". Which of the following is the simplest equivalent symbolism of the statement "Kara is Asian or if Kara is not Asian then Mia is American"?

 

 

 

20. A statement that does not contain any logical connective is called

 

 

21. Rewrite the statement "Every picture tells a story" in an "if-then" form of statement.

 

 

22. Logically, "not both" and "both not" mean the same.

 

 

23. Let S: The sunroof is extra.

R: The radial tires are included.

W: Power windows are optional.

Give the appropriate symbolism (unsimplified) for the statement "If the radial tires are not included, then either the sunroof is not extra or the power windows are not optional".

 

 

 

24. The statement "The number 1 is neither an odd nor an even" is a disjunction.

 

 

 

25.    The statement [(P → Q) ^ P] → Q is not a valid argument.

 

 

 

26. Let A be the statement "Kara is Asian" and B be the statement "Mia is American". Which of the following is the simplest equivalent symbolism for the statement "Either Kara is Asian and Mia is American, or neither Kara is Asian nor Mia is American"?

 

 

 

 

 

27. How will you write the statement "It is not true that either I am wise or you are a fool" into a logically equivalent statement?

 

 

 

 

 

28. Write the converse of the statement "If I get 80% in the final exam, then I will get a certificate of completion".

 

 

 

 

 

29. Let P(x) means "x is a freshman" and Q(x) means "x is a math major". Write the statement "Some freshmen are math majors" in symbolic form.

 

 

 

 

30. Rewrite the statement "Jesse will be a liberal when pigs fly" into an "If-Then" form of statement.

 

 

 

 

31. Let P(x) means "x is a freshman" and Q(x) means "x is a math major". Write the statement "Every math major is a freshman" in symbolic form.

 

 

 

32. The compound statement left parenthesis P logical or Q right parenthesis rightwards arrow left parenthesis P logical and not R right parenthesis is true EXCEPT in which case?

 

 

 

 

33. Consider a propositional language where

P: Paola is happy.

Q: Paola paints a picture.

R: Renzo is happy.

 

Formalize into symbols the following sentence: "If Paola is happy ,then she paints a picture".

 

 

34. What is the truth value of the statement "If 2 is even then every prime number is odd then "?

 

 

 

35. Write the inverse of the statement "If I get 80% in the final exam, then I will get a certificate of completion".