Activity 2.1.
Write an English language statement that has the logical form
Activities 2.4 Activities
Activity 2.2.
What do you think DeMorgan’s Laws would say about
Activity 2.3.
Activity 2.4.
Recall that a pair of coordinates
Consider the following conditional statement.
If Cartesian pointsand are actually the same point, then
(a)
Write out the converse, inverse, and contrapositive of the above statement.
(b)
You now have four conditional statements. For each of the four, decide whether it is true, and justify your answer.
(c)
For each of the three new conditional statements from Task a in turn, take the view that that statement is the original conditional, and decide which of the others are its converse, inverse, and contrapositive.
Activity 2.5.
In this activity, we will justify the equivalence
So consider the statements
(a)
Argue that if
Do not use the proposed equivalence above as part of your argument.
(b)
Argue that if
Do not use the proposed equivalence above as part of your argument.
(c)
Activity 2.6.
Consider the statements
Use propositional calculus and substitution to show that these two statements are equivalent.
