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COMP2781/8781: Statement Forms are Tautologies - Computer Mathematics Assessment Answer
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Subject Code: COMP2781/8781
Q2. Are these system specifications consistent? ”The router can send packets to the edge system only if it supports the new address space. For the router to support the new address space it is necessary that the latest software release be installed. The router can send packets to the edge system if the latest software release is installed. The router does not support the new address
space.”
Q3. Prove or disprove the following statements. Clearly indicate what kind of proof technique you are attempting. For example, you can start like ”We use proof by contradiction”, or ”We use case analysis” etc. Remember that a good proof is more like an essay and not a sequence of formulas without explanations, and you should always complete your proof explaining why the
original claim follows.
Q4. Prove that if n is an odd integer, then
Q5. Determine the truth value od each statement assuming that x, y ? R.
Q6. Show that if n is an integer and n 3 +5 is odd, then n is even using (a) a proof by contradiction, (b) a proof by contraposition. Carefully explain all steps of your proofs and comment on their similarities.
Computer Mathematics Assessment Answer
TASK: Q1. Check whether the following statement forms are tautologies or not without using truth table technique.
Q2. Are these system specifications consistent? ”The router can send packets to the edge system only if it supports the new address space. For the router to support the new address space it is necessary that the latest software release be installed. The router can send packets to the edge system if the latest software release is installed. The router does not support the new address
space.”
Q3. Prove or disprove the following statements. Clearly indicate what kind of proof technique you are attempting. For example, you can start like ”We use proof by contradiction”, or ”We use case analysis” etc. Remember that a good proof is more like an essay and not a sequence of formulas without explanations, and you should always complete your proof explaining why the
original claim follows.
Q4. Prove that if n is an odd integer, then
Q5. Determine the truth value od each statement assuming that x, y ? R.
Q6. Show that if n is an integer and n 3 +5 is odd, then n is even using (a) a proof by contradiction, (b) a proof by contraposition. Carefully explain all steps of your proofs and comment on their similarities.
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