Write the following statements in symbolic form and write their negatins : (1) Mangoes are delicious, but expensive. (2) A person is rich if and only

Question

Write the following statements in symbolic form and write their negatins : (1) Mangoes are delicious, but expensive. (2) A person is rich if and only

Write the following statements in symbolic form and write their negatins :
(1) Mangoes are delicious, but expensive.
(2) A person is rich if and only if he is a software engineer.
(3) If diagonals of a parallelogram are perpendicular, then it is a rhombus. solution :

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Let p : Diagonals of parallelogram are perpendicular.
q : It is a rhombus.
`:.` The given statement is `p""iffq`.
Its negation is `p^^~q`.
i.e., diagonals of a parallelogram are perpendicular but it is not a rhombus.
(b) Let p : Mangoes are delicious.
q : Mangoes statement is `p""iffq`.
`:.` Its negation is `~pvv~q`
i.e., Mangoes are not delicious or they are not expensive.
(c) Let p : A person is rich.
q : He is a software engineer.
`:.` Symbolic form of the given statement is `p""iffq`.
`:.` Its negation is `((p^^~q)vv(q^^~p)`.
i.e., a person is rich and he is not a software engineer or a person is software engineer and he is not rich.