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You have to solve the programming solution in bellow and explain in the picture the general overview.
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01-03 Discrete Review – Sets – Elements and
Subsets
(For more practice problems with answers see:
https://www.khanacademy.org/math/in-in-grade-11-ncert/x79978c5cf3a8f108:sets/x79978c5cf3a8f108:subsets/e
/elements-and-subsets
Problem 6:
For each of the following statements select “yes” or “no” :
Questions about ⊆
a. Is c ⊆ {a, bc , d} ?
Yes No
b. Is {c} ⊆ {a, bc, d} ?
Yes No
c. Is c ⊆ {a, {bc}, d} ?
Yes No
d. Is {c} ⊆ {a, {bc}, d} ?
Yes No
e. Is {bc} ⊆ {a, {bc}, d} ?
Yes No
Is {a, d} ⊆ {a, {bc}, d} ?
Yes No
f.
g. Is { } ⊆ {a, {bc}, d} ?
Yes No
h. Is ⊆ {a, {bc}, , d} ?
i.
Is { } ⊆ {a, {bc}, , d} ?
Yes
Yes
No
No
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
Questions about ∈
j.
Is c ∈ {a, bc , d} ?
Yes No
k. Is {c} ∈ {a, bc, d} ?
Yes No
Is c ∈ {a, {bc}, d} ?
Yes No
m. Is {c} ∈ {a, {bc}, d} ?
Yes No
n. Is {bc} ∈ {a, {bc}, d} ?
Yes No
o. Is {a, d} ∈ {a, {bc}, d} ?
Yes No
p. Is { } ∈ {a, {bc}, d} ?
Yes No
l.
q. Is ∈ {a, {bc}, , d} ?
r. Is { } ∈ {a, {bc}, , d} ?
Yes
Yes
No
No
Problem 7:
(Book problem 3 (p. 37))
Let A = {a, ∅}. Answer true or false for each of the following statements.
a. a ∈ A.
b. {a} ∈ A.
c. a ⊆ A.
d. {a} ⊆ A.
e. ∅ ⊆ A.
f. ∅ ∈ A.
g. {∅} ⊆ A.
h. {∅} ∈ A.
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
Problem 8:
Introduction:
In class we drew pictures that represented sets, for example, we drew the following set:
{ a, b, {b}, {c, d}, e, { }, {{f, g},h}, i}
like this:
Problem: Draw a picture like the ones we drew in class (i.e. like the one pictured above) for each of the
following sets:
a. {p, h, o, n, e}
b. {ph, one}
c. {{}, {p,h,o,n,e}}
d. {{p, h, o, n, e}}
e. {{∅, p, h, o}, ne}
f. {{∅, ph, {o}}, ne}
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
Problem 9
Let T = {a, {a,b}, {a, {b, c}}, ∅, c}
For each of the following problems, select from one of the following answers:
S
Subset of T (but not an element of T)
E
Element of T (but not a subset of T)
B
Both a subset of T and an element of T
N
Neither a subset of T nor an element of T
a. a
b. b
c. c
d. ∅
e. {a}
f.
{b}
g. {c}
h. {∅}
i.
{b,a}
j.
{c, b}
k. {a, b, c}
l.
{a, {b,c}}
m. {{a}}
n. {{b,a}}
o. {{b,c}}
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
Problem 10
Let S = {a, {b,c,d},∅ , {∅}, {g, ∅}, h, {i}}
a. Is ∅ ∈ S ?
b. Is ∅ ⊆ S ?
c. Is {a} ∈ S ?
d. Is {a} ⊆ S ?
e. Is i ∈ S ?
f.
is i ⊆ S ?
g. Is {i} ∈ S ?
h. Is {i} ⊆ S ?
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
Problem Set 01-01
Discrete Review – Truth Tables
Want more practice? Self-test problems for Truth Tables with answers can be found here:
https://numbas.mathcentre.ac.uk/question/134833/truth-tables-question/embed/
NOTE: I’ve left you space between the problems so you can print this out and write out your answers
and then save them for review later!!
Problem 1:
There is no problem 1.
You can expect the numbering in my homework assignments to be weird. But hopefully the numbers on the
solutions are the same as the numbers of the problems!!
Problem 2:
Create a truth table (using the approach demonstrated in class – i.e. you must show your work the way I do it)
for the following logical expression:
(p→q)∧(p→r)
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
Problem 3:
Create truth tables (using the approach demonstrated in class – i.e. you must show your work) that
confirm the following equivalences.
Then circle or highlight the two columns on your truth table that have the left and right side of the
equivalences.
a. ¬(p∧q) ≡ (¬p ∨ ¬q)
b. ¬(p∨q) ≡ (¬p ∧ ¬q)
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
c. ((¬q→¬p)∨(p∨¬q))∧¬p ≡ ¬p
d. ((¬p∧q)∨(p→q))∧¬q ≡ (¬p ∧ ¬q)
Copyright © 2024, Jennifer S. Kay, [email protected]
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the author.
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