Question 1: Let p, q and r denote the propositions 'My computer has 512 MB of memory', 'My computer has 1 GB of memory' and 'My computer runs Windows Vista', respectively. (a) Write down an English sentence that corresponds to the proposition -r^p. (b) Write down an English sentence that corresponds to the proposition q !-p. (c) Express the proposition 'If my computer has 1 GB of memory, then either my computer runs Windows Vista and does not have 512 MB of memory, or my computer does not run Windows Vista' in symbolic form.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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![Question 1: Let p, q and r denote the propositions 'My computer has 512 MB of
memory', 'My computer has 1 GB of memory' and 'My computer runs
Windows Vista', respectively.
(a) Write down an English sentence that corresponds to the proposition r^p.
(b) Write down an English sentence that corresponds to the proposition q !-p.
(c) Express the proposition 'If my computer has 1 GB of memory, then either my
computer runs Windows Vista and does not have 512 MB of memory, or my
computer does not run Windows Vista' in symbolic form.
Question 2: Give the truth table for each of the following expressions:
(a) -(p v-q) vp
(b) [p→ (p ^ q)] →¬
(c) (p ^ q) <→ (¬p v ¬9)
(d) [(p ^ r) v (q ^ r)] → (p → ¬q)
Question 3: Write down English sentences for the converse and contrapositive of the
proposition
'If Salalah is in Oman, then Dubai is not in Japan'.
Converse:
Contrapositive:
Question 4:
(a) Give the truth table for the expression q ^ [(-pv q)→.
(b) State, with brief reasons, whether q A [(-p v q) - q is a tautology, a
contradiction, or neither.
Question 5: Use the laws of logic to simplify -[q→-(p^q)].
Question 6: Suppose p denotes 'I ride my bicycle regularly' and q denotes 'I have an
injured knee'.
(a) Write down in words the argument that has symbolic form [q ^(-→p)]→-p.
(b) Use truth table to determine if the argument is valid.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fc93b34-e213-4100-9a27-7540e66f1793%2Fab72eecf-9e8c-48a8-82ab-11b22b667d79%2F7i6g6v_processed.jpeg&w=3840&q=75)
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