Question

Write the proposition "the product of two irrational numbers is irrational" in symbolic logic notation.

a) ∀a,b∈I∀a,b∈I
b) ∃a,b∈I∃a,b∈I
c) ∀a,b∉I∀a,b∈/I
d) ∃a,b∉I∃a,b∈/I

Answer 1

In symbolic logic notation, the proposition 'the product of two irrational numbers is irrational' can be represented as: (∀a,b)((a ∉ Q) ∧ (b ∉ Q) ∧ (a × b ∉ Q)).

Step-by-step explanation:

In symbolic logic notation, the proposition 'the product of two irrational numbers is irrational' can be represented as:

(∀a,b)((a ∉ Q) ∧ (b ∉ Q) ∧ (a × b ∉ Q))

Here, Q represents the set of rational numbers and ∉ represents 'not a member of'. The proposition states that for all a and b, if a and b are not irrational numbers and their product is not a rational number, then the product of a and b is irrational.