truth table: Binary Operations 5

requirements

more examples

security alarm

if the inputs are

is there motion?
is the code right?

alarm	motion, wrong code	motion, right code	no motion, wrong code	no motion, right code	operation
alarm always off	off	off	off	off	contradiction
motion and wrong code	on	off	off	off	logical_conjunction
wrong code	on	off	on	off	project_second
(no motion) and wrong code	off	off	on	off	converse_non_implication
no motion	off	off	on	on	negate_first
not (motion and wrong code)	off	on	on	on	logical_nand
alarm always	on	on	on	on	tautology
motion or right code	on	on	on	off	logical_disjunction
(not (motion and wrong code)) and (motion or wrong code)	off	on	on	off	exclusive_disjunction
motion and right code	off	on	off	off	material_non_implication
motion	on	on	off	off	project_first
motion or right code	on	on	off	on	converse_implication
right code	off	on	off	on	negate_second
not (motion or wrong code)	off	off	off	on	logical_nor
(no motion or wrong code) and (motion or right code)	on	off	off	on	logical_equality
no motion or wrong code	on	off	on	on	material_implication

operation	rule
contradiction	alarm always off
logical_conjunction	alarm only if there is motion and the code is wrong
project_second	alarm only if the code is wrong
converse_non_implication	alarm only if there is no motion and the code is wrong
negate_first	alarm only if there is no motion
logical_nand	alarm off only if there is motion and the code is wrong
tautology	alarm always on
logical_disjunction	alarm off if there is no motion and the code is right
exclusive_disjunction	alarm off if there is motion and the code is wrong, alarm off if there is no motion and the code is right
material_non_implication	alarm only if there is motion and the code is right
project_first	alarm only if there is motion
converse_implication	alarm off only if there is no motion and the code is wrong
negate_second	alarm only if the code is right
logical_nor	alarm only if there is no motion and the code is right
logical_equality	alarm if there is motion and the code is wrong, alarm if there is no motion and the code is right
material_implication	alarm off only if there is motion and the code is right

hiring

if the inputs are

is the person a strong option?
is the person a strong fit?

hire/reject	strong option, strong fit	strong option, weak fit	weak option, strong fit	weak option, weak fit	operation
reject	reject	reject	reject	reject	contradiction
strong option and strong fit	hire	reject	reject	reject	logical_conjunction
strong fit	hire	reject	hire	reject	project_second
weak option and strong fit	reject	reject	hire	reject	converse_non_implication
weak option	reject	reject	hire	hire	negate_first
not (strong option and strong fit)	reject	hire	hire	hire	logical_nand
hire	hire	hire	hire	hire	tautology
strong option or weak fit	hire	hire	hire	reject	logical_disjunction
(not (strong option and strong fit)) and (strong option or strong fit)	reject	hire	hire	reject	exclusive_disjunction
strong option and weak fit	reject	hire	reject	reject	material_non_implication
strong option	hire	hire	reject	reject	project_first
strong option or weak fit	hire	hire	reject	hire	converse_implication
weak fit	reject	hire	reject	hire	negate_second
not (strong option or strong fit)	reject	reject	reject	hire	logical_nor
(weak option or strong fit) and (strong option or weak fit)	hire	reject	reject	hire	logical_equality
weak option or strong fit	hire	reject	hire	hire	material_implication

operation	rule
contradiction	not hiring
logical_conjunction	hire only if it is a strong option that is a strong fit
project_second	hire only if it is a strong fit
converse_non_implication	hire only if it is weak option that is a strong fit
negate_first	hire only if it is weak option
logical_nand	reject only if it is a strong option that is a strong fit
tautology	hiring
logical_disjunction	reject only if it is weak option that is a weak fit
exclusive_disjunction	reject if it is a strong option that is a strong fit, reject if it is a weak option that is a weak fit
material_non_implication	hire only if it is a strong option that is a weak fit
project_first	hire only if it is a strong option
converse_implication	reject only if it is weak option that is a strong fit
negate_second	hire only if it is a weak fit
logical_nor	hire only if it is a weak option that is a weak fit
logical_equality	hire if it is a strong option that is a strong fit, hire if it is weak option that is a weak fit
material_implication	reject only if it is a strong option that is a weak fit

store discount policy

if the inputs are

does the person have a coupon?
is the person a member?

discount/regular price	coupon, member	coupon, not member	no coupon, member	no coupon, not member	operation
regular	regular	regular	regular	regular	contradiction
coupon and member	discount	regular	regular	regular	logical_conjunction
member	discount	regular	discount	regular	project_second
no coupon and member	regular	regular	discount	regular	converse_non_implication
no coupon	regular	regular	discount	discount	negate_first
not (coupon and member)	regular	discount	discount	discount	logical_nand
discount	discount	discount	discount	discount	tautology
coupon or not member	discount	discount	discount	regular	logical_disjunction
(not (coupon and member)) and (coupon or member)	regular	discount	discount	regular	exclusive_disjunction
coupon and not member	regular	discount	regular	regular	material_non_implication
coupon	discount	discount	regular	regular	project_first
coupon or not member	discount	discount	regular	discount	converse_implication
not member	regular	discount	regular	discount	negate_second
not (coupon or member)	regular	regular	regular	discount	logical_nor
(no coupon or member) and (coupon or not member)	discount	regular	regular	discount	logical_equality
no coupon or member	discount	regular	discount	discount	material_implication

operation	rule
contradiction	everyone pays regular price, no discounts
logical_conjunction	discount price only if person has a coupon and is a member
project_second	discount price only if person is a member
converse_non_implication	discount price only if person does not have a coupon and is a member
negate_first	discount price only if person does not have a coupon
logical_nand	regular price only if person has a coupon and is a member
tautology	everyone gets a discount
logical_disjunction	regular price only if person does not have a coupon and is not a member
exclusive_disjunction	regular price if person has a coupon and is a member, regular price if person does not have a coupon and is not a member
material_non_implication	discount price only if person has a coupon and is not a member
project_first	discount price only if person has a coupon
converse_implication	regular price only if person does not have a coupon and is a member
negate_second	discount price only if person is not a member
logical_nor	discount price only if person does not have a coupon and is not a member
logical_equality	discount price only if person has a coupon and is a member, discount price if person does not have a coupon and is not a member
material_implication	regular price only if person has a coupon and is not a member

watering plants

if the inputs are

is the soil dry?
did it rain?

water the plants	dry soil, no rain	dry soil, it rained	wet soil, no rain	wet soil, it rained	operation
do not water	no	no	no	no	contradiction
dry soil and no rain	yes	no	no	no	logical_conjunction
no rain	yes	no	yes	no	project_second
wet soil and no rain	no	no	yes	no	converse_non_implication
wet soil	no	no	yes	yes	negate_first
not (dry soil and no rain)	no	yes	yes	yes	logical_nand
water	yes	yes	yes	yes	tautology
dry soil or it rained	yes	yes	yes	no	logical_disjunction
(not (dry soil and no rain)) and (dry soil or no rain)	no	yes	yes	no	exclusive_disjunction
dry soil and it rained	no	yes	no	no	material_non_implication
dry soil	yes	yes	no	no	project_first
dry soil or it rained	yes	yes	no	yes	converse_implication
rain	no	yes	no	yes	negate_second
not (dry soil or no rain)	no	no	no	yes	logical_nor
(wet soil or no rain) and (dry soil or it rained)	yes	no	no	yes	logical_equality
(wet soil) or no rain	yes	no	yes	yes	material_implication

operation	rule
contradiction	do not water
logical_conjunction	water only if soil is dry and it did not rain
project_second	water only if it did not rain
converse_non_implication	water only if soil is wet and it did not rain
negate_first	water only if soil is wet
logical_nand	do not water if soil is dry and it did not rain
tautology	everyone gets a yes
logical_disjunction	do not water if soil is wet and it rained
exclusive_disjunction	do not water if soil is dry and it did not rain, do not water if soil is wet and it did not rain
material_non_implication	water only if soil is dry and it rained
project_first	water only if soil is dry
converse_implication	do not water if soil is wet and it did not rain
negate_second	water only if it rained
logical_nor	water only if soil is wet and it rained
logical_equality	water only if soil is dry and it did not rain, water if soil is wet and it did not rain
material_implication	do not water if soil is dry and it rained

what is next?

Would you like to test the truth table tests?

rate pumping python

If this has been a 7 star experience for you, please CLICK HERE to leave a 5 star review of pumping python. It helps other people get into the book too