UGRD-CS6105 Discrete Mathematics Study Guide 2023
with complete solution
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
Every natural number greater than 1 is either prime or composite.
molecular
conditional
In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One
is a square, and the other is a triangle. Each shape is drawn in a single color.
Suppose you believe me when I tell you that if the square is blue, then the triangle
is green. What do you therefore know about the truth value of the following
statement?
If the triangle is not green, then the square is not blue.
true
Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}
Find A U B
{1, 2, 3, 4, 5, 6, 7}
In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One
is a square, and the other is a triangle. Each shape is drawn in a single color.
Suppose you believe me when I tell you that if the square is blue, then the triangle
is green. What do you therefore know about the truth value of the following
statement?
The square and the triangle are both green.
false
Let A = {3, 4, 5}. Find the cardinality of P(A).
8
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
The Broncos will win the Super Bowl or I'll eat my hat.
molecular
conjunction
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
Everybody needs somebody sometime.
, atomic
n/a
Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}
Find A ∩ B
{3, 4, 5}
The cardinality of {3, 5, 7, 9, 5} is 5.
False
Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}
Find A \ B
{1, 2}
Determine whether the sentence below is an atomic statement, a molecular
statement, or not a statement at all.
The customers wore shoes and they wore socks.
molecular
Find |A ∩ B| when A = {1, 3, 5, 7, 9} and B {2, 4, 6, 8, 10}
0
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
We can have donuts for dinner, but only if it rains.
molecular
conditional
Find the cardinality of S = {1, {2,3,4},0}
3
Find | R | when R = {2, 4, 6,..., 180}
90
Find the cardinality of R = {20,21,...,39, 40}
21
Determine whether the sentence below is an atomic statement, a molecular
statement, or not a statement at all.
Customers must wear shoes.
Not a statement
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
The sum of the first 100 odd positive integers.
atomic
n/a
Determine whether the sentence below is an atomic statement, a molecular
statement, or not a statement at all.
with complete solution
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
Every natural number greater than 1 is either prime or composite.
molecular
conditional
In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One
is a square, and the other is a triangle. Each shape is drawn in a single color.
Suppose you believe me when I tell you that if the square is blue, then the triangle
is green. What do you therefore know about the truth value of the following
statement?
If the triangle is not green, then the square is not blue.
true
Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}
Find A U B
{1, 2, 3, 4, 5, 6, 7}
In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One
is a square, and the other is a triangle. Each shape is drawn in a single color.
Suppose you believe me when I tell you that if the square is blue, then the triangle
is green. What do you therefore know about the truth value of the following
statement?
The square and the triangle are both green.
false
Let A = {3, 4, 5}. Find the cardinality of P(A).
8
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
The Broncos will win the Super Bowl or I'll eat my hat.
molecular
conjunction
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
Everybody needs somebody sometime.
, atomic
n/a
Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}
Find A ∩ B
{3, 4, 5}
The cardinality of {3, 5, 7, 9, 5} is 5.
False
Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}
Find A \ B
{1, 2}
Determine whether the sentence below is an atomic statement, a molecular
statement, or not a statement at all.
The customers wore shoes and they wore socks.
molecular
Find |A ∩ B| when A = {1, 3, 5, 7, 9} and B {2, 4, 6, 8, 10}
0
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
We can have donuts for dinner, but only if it rains.
molecular
conditional
Find the cardinality of S = {1, {2,3,4},0}
3
Find | R | when R = {2, 4, 6,..., 180}
90
Find the cardinality of R = {20,21,...,39, 40}
21
Determine whether the sentence below is an atomic statement, a molecular
statement, or not a statement at all.
Customers must wear shoes.
Not a statement
Classify the sentence below as an atomic statement, a molecular statement, or
not a statement at all. If the statement is molecular, identify what kind it is
(conjuction, disjunction, conditional, biconditional, negation).
The sum of the first 100 odd positive integers.
atomic
n/a
Determine whether the sentence below is an atomic statement, a molecular
statement, or not a statement at all.
