(1) Use inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? ...and 4 other questions.

1) Use inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? (I don't seem to find a pattern?) 2) Find the counterexample to show that the following statemnet is incorrect. "the sum of any odd numbers is divisible by 4. ( I tried several odd numbers and the answer is always divisible by 4) 3) Sandra drove for 234.8 miles and used 12.6 gallons of gas. estimate the number of miles Sandra's car get per gallon? ( will the answer be as simple as 234.8 / 12.6 = 18.6 miles per gallon?) 4) Sam founda number of nickles and dimes, and quarters in his room. he found thre more dimes than nickles but twice as many quartes as dimes. The total value of coins was... click for more

Truth tables and De Morgan's Laws

1) Construct a truth table and determine the truth value of the statement ~ q = { ~r ^ ( p v q) }, when p is false, q is true and r is true. 2) Use De Morgan's Laws to determine whether the two statements are equivalent. ~( p ^ q), ~(q v ~p) 3) Determine which, if any of the three statements are equivalent. a) If today is Monday, then tomorrow is not Wednesday b) It is false that today is Monday and tomorrow is not Wednesday c) today is not Monday or tomorrow is Wednesday.

Logic and validity of arguments

Hi Shrikant, I wonder if your can help me with this: 1) Determine whether the argument is valid or invalid. A tree as green leaves or the tree does not produce oxygen. This tree has green leaves. ------------------------------------------------------------- Therefore:. This tree does not produce oxygen. 2) Use Euler Diagrams to determine whether the following syllogism is valid or invalid. Some senators are conservationists No conservationists are pro-development ------------------------------------------ Therefore: some senators are not pro-development. 4) Determine the truth value of the following statement: Rembrandt... click for more

In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants. No students shook hands with their own partners. After the fair, the students discussed the project they have visited. Hannah learned that no two of the other eleven students had shaken the same number of hands. How many hands did Hannah's partner shake?

In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants. No students shook hands with their own partners. After the fair, the students discussed the project they have visited. Hannah learned that no two of the other eleven students had shaken the same number of hands. How many hands did Hannah's partner shake?

Combinatorial Analysis

I have attached chapter 1 description pages. I need following problems. Page 16 : - Problem Number: - 10 Page 17: - Problem Number: - 15 Page 19: - Problem Numbers :- 5 and 8 Please mention each and every step. Thanking you