logic symbols conincontra truth tables i 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500...
TRANSCRIPT
Logic Symbols
CONINCONTRA
Truth Tables I
100
200
300
400
500
100200
300
400
500
100
200
300
400
500
Old Stuff
100200
300
400
500
ss: you choose a salad,: you choose a salad,mm: you choose a meat dish : you choose a meat dish
(main course),(main course),dd: you choose a dessert.: you choose a dessert.
You choose a You choose a twotwo course meal course meal which which mustmust include a main include a main
course and either a salad or a course and either a salad or a dessert, but not both.dessert, but not both.
Write the sentence above using Write the sentence above using logic symbols.logic symbols.
ss: you choose a salad,: you choose a salad,mm: you choose a meat : you choose a meat dish (main course),dish (main course),dd: you choose a dessert: you choose a dessert
Write in words Write in words ss dd..
Two logic propositions are Two logic propositions are given.given.
pp: Paula eats chocolates.: Paula eats chocolates.qq: Paula watches television.: Paula watches television.
qq pp..
Three propositions p, q and r are defined as follows:p: the water is cold.
q: the water is boiling.r: the water is warm.Write the following sentence as a logic
statement using symbols only."The water is cold if and only if it is
neither boiling nor warm"
Three propositions p, q and r are defined as follows:
p: the water is cold.q: the water is boiling.
r: the water is warm.Write one sentence, in words,
for the following logic statement:
rqp )(
Write down, in words, the Write down, in words, the converse of the statementconverse of the statement“If the sun is shining then I “If the sun is shining then I
will walk to school.”will walk to school.”
Consider the statement Consider the statement ““If I am tired, then I went to If I am tired, then I went to
bed late.bed late.”Write down its contrapositive.
Let Let pp and and qq be the statements be the statementsp: you watch the music TV p: you watch the music TV
channelchannelq: you like musicq: you like music
Consider the following logic Consider the following logic statement.statement.
If you watch the music TV channel If you watch the music TV channel then you like music.then you like music.
Write down in words the inverse Write down in words the inverse of the statement.of the statement.
““If a figure is a square, then it is a If a figure is a square, then it is a rhombus”rhombus”..
(a)(a) For this statement, write in For this statement, write in words words
(i)(i) its converse;its converse;(ii)(ii) its inverse;its inverse;
(iii)(iii) its contrapositive.its contrapositive.
(b)(b) Only one of the statements in Only one of the statements in part(a) is true. Which one is it?part(a) is true. Which one is it?
The compound proposition The compound proposition 22xx + 3 = 5 + 3 = 5 xx22 = = xx is is
given.given. Write down the converse of Write down the converse of this compound proposition.this compound proposition.Give an example to show Give an example to show that the converse is false.that the converse is false.
Complete the truth tableComplete the truth tablep q p pq
p q qp qp p pqp )( qpqp )(
What word is described by the above compound proposition?
Consider two propositions Consider two propositions pp and and qq. Complete the . Complete the
truth table below for the truth table below for the compound proposition.compound proposition.
)()( qpqp
Consider the following Consider the following statements.statements.
p: students work hardp: students work hardq: students will succeedq: students will succeed
If students do not work hard, If students do not work hard, then they will not succeed.then they will not succeed.
Complete a truth table, relating Complete a truth table, relating to the statement above and to the statement above and
decide whether the statement is decide whether the statement is logically valid.logically valid.
pp: Alex is from Uruguay: Alex is from Uruguayqq: Alex is a scientist: Alex is a scientist
rr: Alex plays the flute: Alex plays the flute
Is the following argument logically valid? Write what the argument is saying in
words.
)( pqr
The sports offered at a retirement village are The sports offered at a retirement village are Golf (Golf (GG), Tennis (), Tennis (TT) and Swimming () and Swimming (SS). The Venn ). The Venn diagram shows the numbers of people involved diagram shows the numbers of people involved
in each activity. How many peoplein each activity. How many people(i) only play golf?(i) only play golf?
(ii)play both tennis and golf?(ii)play both tennis and golf?
(iii)do not play golf?(iii)do not play golf?
G T
S
11
1
2
34
84
6
A bag contains 2 red, 3 yellow and 5 A bag contains 2 red, 3 yellow and 5 green sweets.green sweets.
Without looking, Mary takes one Without looking, Mary takes one sweet out of the bag and eats it. She sweet out of the bag and eats it. She
then takes out a second sweet.then takes out a second sweet.(a)(a) If the first sweet is green, what If the first sweet is green, what is the probability that the second is the probability that the second
sweet is also green?sweet is also green?(b)(b) If the first sweet is not red, what If the first sweet is not red, what
is the probability that the second is the probability that the second sweet is red?sweet is red?
Chocos Zucos Fruti Total
Buenos Aires
43 85 62 190
Montevido 57 35 118 210
Total 100 120 180 400
A survey of 400 people is carried out by a A survey of 400 people is carried out by a market research organization in two different market research organization in two different cities, Buenos Aires and Montevideo. The people cities, Buenos Aires and Montevideo. The people are asked which brand of cereal they prefer out are asked which brand of cereal they prefer out of Chocos, Zucos or Fruti. The table below of Chocos, Zucos or Fruti. The table below summarizes their responses.summarizes their responses. One person is chosen at random from those One person is chosen at random from those surveyed. Find the probability that this personsurveyed. Find the probability that this persondoes not prefer Zucos.does not prefer Zucos.
A survey of 400 people is carried out by a market A survey of 400 people is carried out by a market research organization in two different cities, research organization in two different cities,
Buenos Aires and Montevideo. The people are Buenos Aires and Montevideo. The people are asked which brand of cereal they prefer out of asked which brand of cereal they prefer out of
Chocos, Zucos or Fruti. The table below Chocos, Zucos or Fruti. The table below summarizes their responses.summarizes their responses.
One person is chosen at random from those One person is chosen at random from those surveyed.surveyed.
prefers Chocos, given that they live in prefers Chocos, given that they live in Montevideo.Montevideo.
Chocos Zucos Fruti Total
Buenos Aires
43 85 62 190
Montevido 57 35 118 210
Total 100 120 180 400
A survey of 400 people is carried out by a market A survey of 400 people is carried out by a market research organization in two different cities, research organization in two different cities,
Buenos Aires and Montevideo. The people are Buenos Aires and Montevideo. The people are asked which brand of cereal they prefer out of asked which brand of cereal they prefer out of
Chocos, Zucos or Fruti. The table below Chocos, Zucos or Fruti. The table below summarizes their responses.summarizes their responses.
Two people are chosen at random from those Two people are chosen at random from those surveyed. Find the probability that they both surveyed. Find the probability that they both
prefer Fruti.prefer Fruti.
Chocos Zucos Fruti Total
Buenos Aires
43 85 62 190
Montevido 57 35 118 210
Total 100 120 180 400