⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠ You can decompress Drawing data with the command palette: ‘Decompress current Excalidraw file’. For more info check in plugin settings under ‘Saving’
Excalidraw Data
Text Elements
for each of the following statements determine whether it is a proposition. answer yes or no
a proposition is a declarative statement that can hold a true or false value. if there is a variable, or a explanation point, or sking a question, just no true or false, it is not a proposition
sum of two odd numbers is even - true - proposition y + 7 > 10 - not a proposition, tf is y the moon is made of cheese - proposition have a great day - not a proposition, not true or false this is a good book - not a proposition, subjective.
complete truth table for following logical expression: -p ^ (pvq) -p q -p p v q -p ^ (pvq)
t f t f
t t f f
f f t t
t t t f
f f t f
the expression is neither a tautology nor a contrafiction.
U { a,b,c,d,e,f }
A = {a,c,f} B = {b,c,d} C = {a,d,e}
B U C b,c,d,a,e
A n C a
BU(AnC) a,b,c,d
c n -B c n {a,e,f} a,e
B - (AUC) {b,c,d} - ({a,c,f} u {a,d,e}) {b,c,d} - (a,c,d,e,f) b
(A-B) n C {a,c,f} - {b,c,d}) n C {a,c,f} n c a
(-AnC) U B ({b,d,e}n{a,d,e}) U B ({d,e}) U B b,c,d,e
P(A) a,c,f a,c a,f c,f a c f Empty set
empty set is a subset of any set
-(yz) + w(x+-z) -(1*0) + 1(1+0) 1 + 1(1) 1 + 1 1
-w + x + yz -1 + 1 + 1*0 -1 + 1 0 + 1 1
x*-y + -wz + -y 1-1 + -10 + -1 10 + 0*0 + 0 0
|B| means find cardinality
a E X means a is an element of x
so 5 E B 5 is in b so it is 2 E B no, we have {2,5} in b, that is no good though, need just 2
if b = {{2}} 2 E B no
if b = {2} 2 E B yes {2} E B no empty set is not an element in there
if b = {5} {5} C B True C means each individual element within this given set is located within this set empty set always in C always a subset of any set
minterms are equivalent to cases where function is equal to one
“For ALL” or “Every” means upside down A means universal
“Some” or “there exists” means E or existential
yes
no
yes
no
no
t
t
f
f
t
t
f
f
f
f
t
t
t
t
f
f
f
f
t
f
neither
{a,b,c,d,e}
{a}
{a,b,c,d}
{a,e}
{b}
{a}
{a,b,c,d}
{a,c,f}, {a,c}, {a,f}, {c,f}, {a},{c},{f}, {0}
1
Embedded Files
95188a1fbc4e54f35a441779cfc62fbcd3b81dca: page=1
63535d6261140cc1fd19974cffbfbbd37c2760d5: page=2
564a93cf5f547618d5df4d60397dbdad1dcf58a8: page=3
98d3f2a87eb07b3345fffb1fc8b8de047288dd3c: page=4
4babf67093e4071a4e165b3ac5d1f25d659db293: page=5
d47dd902044a472a19b6db16fad10b0dab4724c6: page=6