4.1 Investigate if the following Boolean “identity” is correct, or not. If it is not correct, formulate the correct version of the identity (?′?+?)′=?+?′?′. [2]
4.1 Investigate if the following Boolean “identity” is correct, or not. If it is not correct, formulate the correct version of the identity (?′?+?)′=?+?′?′. [2]
4.2 Use the identities of Boolean algebra to verify the following identity: [4]
?(?+?)+??′+??′+?=?+?+?
4.3 Consider the logic gate circuit below:
a) Formulate the Boolean expression corresponding to the output of the logic circuit diagram above. [2]
b) Hence, show that the Boolean expression formulated in part (a) reduces to ??+?. [3]
c) Draw the logic gate circuit diagram corresponding to the reduced expression in
part (b) above.
3.1 Let r, s, t denote the statements “Joe is registered for MCI511S”, “Joe will go to the zoo next week”, “Joe is registered for PBT512S”, respectively. Translate the symbolic statement (∼?∨?)→∼? into words. [2]
3.2 Write the negation of the statement “If Joe writes the exam, he will go the airport but he will not catch the flight”. [2]
3.3 Determine the truth value of the compound statement (?∧∼?)∨∼?, if p is false, q is true, s is true? [2]
3
3.4 Consider the argument below.
If Aina passes the final exams, then she gets a pay rise.
If Aina gets a pay rise, then she does not look for a second job.
Aina looks for a second job. Therefore, Aina did not pass the final exams. a) Formulate the argument in symbolic form. [2] b) Determine whether the argument is valid, or invalid. Draw a truth table. [
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4.1 Investigate if the following Boolean "identity" is correct, or not. If it is not correct,
formulate the correct version of the identity (x'y + z)' = x + y'z'.
[2]
4.2 Use the identities of Boolean algebra to verify the following identity:
[4]
y(x + z) + xy' + yz' + z = x + y+z
4.3 Consider the logic gate circuit below:
DE
a) Formulate the Boolean expression corresponding to the output of the logic circuit
[2]
diagram above.
b) Hence, show that the Boolean expression formulated in part (a) reduces to AC + B. [3]
c) Draw the logic gate circuit diagram corresponding to the reduced expression in
part (b) above.
[2]
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