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An Approach to Algebra
Claudia Patricia Chapa Tamez
Review activity
1.5.1.1 Compound propositions
Determine the truth value for each proposition p and q , then perform a conjunction between
the pair of propositions.
Conjunction
1. “Honolulu is the capital of Hawaii” and “Berlin is the
capital of Germany”.
p
q
pq
2. “The Moon is Earth's only natural satellite” and “The
Sun is the star at the center of the Universe”.
3. “5+5=15” and “34 is greater than 25”.
4. “The sky is green” and “The grass is blue”.
Determine the truth value for each proposition p and q , then perform a conjunction between
the pair of propositions.
Conjunction
p
q
pq
1. “ 3  4  12 ” and “ 6  5  30 ”
2. “The Statue of Liberty is in Seattle” and “Golden
bridge is at San Francisco”.
3. “1 is a prime number” and “5 is greater than 25”.
4. “-3 is a negative integer” and “0 is a natural number”.
Determine the solution set for each of the given compound propositions.
1)
2)
3)
4)
p( x)  q( x) :" x is prime"" x  10"; x {Digits}
q( x)  r ( x) :" x is even"" x  2"; x  N
p( x)  q( x) :"1  x  5"" x  3"; x  W
p( x)  q( x) :" x  0"" x  0"; x  R
1
D . R . © I n s t it u t o T e c n o l ó g i c o y d e E s t u d i o s Su p e r i o r e s d e M o n t e r r e y , M é x i co 2 0 12
An Approach to Algebra
Claudia Patricia Chapa Tamez
Solution
Determine the truth value for each proposition p and q , then perform a conjunction between
the pair of propositions.
Conjunction
1. “Honolulu is the capital of Hawaii” and “Berlin is the
capital of Germany”.
p
T
q
T
pq
T
2. “The Moon is Earth's only natural satellite” and “The
Sun is the star at the center of the Universe”.
T
F
F
3. “5+5=15” and “34 is greater than 25”.
F
T
F
4. “The sky is green” and “The grass is blue”.
F
F
F
Determine the truth value for each proposition p and q , then perform a conjunction between
the pair of propositions.
Conjunction
3

4

12
1. “
” and “ 6  5  30 ”
2. “The Statue of Liberty is in Seattle” and “Golden
bridge is at San Francisco”.
3. “1 is a prime number” and “5 is greater than 25”.
p
T
F
q
T
T
pq
T
F
F
F
F
4. “-3 is a negative integer” and “0 is a natural
number”.
T
F
F
Determine the solution set for each of the given compound propositions.
1. p( x)  q( x) :" x is prime"" x  10"; x {Digits}
2. q( x)  r ( x) :" x is even"" x  2"; x  N
3. p( x)  q( x) :"1  x  5"" x  3"; x  W
4. p( x)  q( x) :" x  0"" x  0"; x  R
Solution
p( x)  q( x) :" x is prime"" x  10"; x {Digits}
Solution set P  {2,3,5,7} , these are prime numbers that belong to digits numbers
set.
Solution set Q  {0,1,2,3,4,5,6,7,8,9} , these are numbers less than or equal to 10
that belong to digits numbers set.
1)
2
D . R . © I n s t it u t o T e c n o l ó g i c o y d e E s t u d i o s Su p e r i o r e s d e M o n t e r r e y , M é x i co 2 0 12
An Approach to Algebra
Claudia Patricia Chapa Tamez
Then the solution set of the compound proposition is: P  Q  {2,3,5,7} , the set
of elements common for P and Q.
q( x)  r ( x) :" x is even"" x  2"; x  N
Solution set Q  {2,4,6,8,...} , these are even numbers that belong to natural
numbers set.
Solution set R  {1} , it is a number less than 2 that belong to natural numbers
set.
Then the solution set of the compound proposition is: Q  R  { }   , there are
no common elements between Q and R.
p( x)  q( x) :"1  x  5"" x  3"; x  W
Solution set P  {0,1,2,3,4,5} , these are numbers between -1 and 5 that belong to
whole numbers set.
Solution set Q  {4,5,6,7,8,...} , these are numbers greater than 3 that belong to
whole numbers set.
Then the solution set of the compound proposition is: P Q  {4,5} , the set of
elements common for P and Q.
p( x)  q( x) :" x  0"" x  0" ; x  Z
Solution set P  {1,2,3,4,5,...} , these are numbers greater than 0 that belong to
integer numbers set.
Solution set Q  {1,2,3,4,5,...} , these are numbers less than 0 that belong
to integer numbers set.
Then the solution set of the compound proposition is: P  Q  { }   , there are
no common elements between P and Q.
2)
3)
4)
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