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Logic questions

Logic questions | form five Pure Advanced Mathematics

Find Logic examination questions, form five Pure Advanced Mathematics in acaproso.com

# Question
1

Find a sentence having the following truth table:

P Q R S(P,Q,R)
T T T F
T T F T
T F T T
T F F F
F T T T
F T F F
F F T F
F F F T

 


Mathematical Calculation
2

If veebar denotes the exclusive `or` , that is P veebar Q= (P vee Q ) wedge sim(P wedge Q), complete filling the following table:

P Q P veebar Q
T T  
T F  
F T  
F F  

 


Mathematical Calculation
3

Check the validity of the following argument sim p ightarrow (q leftrightarrow sim r), sim r ightarrow sim p, q ightarrow sim r and sim r.


Mathematical Calculation
4

Let A_{pq} denote p wedge q and let Np denote sim p. Write the following propositions using A and N instead of wedge and sim:

  1. sim p wedge q
  2. sim (p wedge sim q)
  3. (sim p wedge q)

Mathematical Calculation
5

Use algebra of propositions to show that (p wedge q) vee [sim r wedge (q wedge p)] equiv p wedge q.


Mathematical Calculation
6
  1. Using letters and logical connectives , write the folliwing statement. “If x is less than zero then it is not positive”.
  2. Using the statement given in question (a), find and simplify:
  1. The contrapositive of its inverse
  2. The converse of its contrapositive
  3. Comment on the resulting statements in (b) (i) above.

Mathematical Calculation
7

Given the statement : “If two vectors are orthogonal then their scalar (dot) product is zero”. Write its;

  1. inverse
  2. converse
  3. contrapositive.

Mathematical Calculation
8

Determine the truth values of the following sentences:

  1. Either 2<1 or 2-7 not equal to -5.
  2. If 2+1=10 then 12>10.

Mathematical Calculation
9

Given that S_{1}=(p ightarrow q) ightarrow (sim q ightarrow sim p) and S_{2}= sim ( sim q ightarrow sim p) ightarrow sim (p ightarrow q) use truth tables to find whether or not S1 is equivalent to S2.


Mathematical Calculation
10

Write the statement (sim p ightarrow q) ightarrow (sim q ightarrow sim p) using the connective sim and vee , and prepare a truth table for the reulting disjunction.


Mathematical Calculation