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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 pq 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 pq 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 pq 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 pq 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) 3 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