What is the logical translation of the statement "All boys are male"

• ∃x(B(x)∧M(x) )
• ∀x(B(x)∨M(x) )
• ∀x(B(x)∧M(x) )
• ∀x(B(x)→M(x) )
• ∀x(B(x)→M(x) )

What is the logical translation of the statement following statement? "None of my friends are perfect"

• ∃x(F(x)∧¬P(x) )
• ∃x(¬F(x)∧P(x) )
• ∃x(¬F(x)∧¬P(x) )
• ¬∃x(F(x)∧P(x) )
• ¬∃x(F(x)∧P(x) )

What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational”

• ∃x(real(x)∨rational(x) )
• ∀x(real(x)→rational(x) )
• ∃x(real(x)∧rational(x) )
• ∃x(rational(x)→real(x) )
• ∃x(real(x)∧rational(x) )

What is the HCF of 135 and 225?

• 35
• 90
• 45
• 2
• 45

What is the first order predicate calculus statement equivalent to the following? "Everyone is liked by Someone." Where likes(x, y) represent x likes y.

• ∃y [∀x Likes (x, y)]
• ∀x [∃y Likes (x, y)]
• ∀x [∃y Likes (y, x)]
• ∃x [∃y Likes (x, y)]
• ∀x [∃y Likes (y, x)]

int main() { int x, y = 3, z = 0; x = x == y+2 == z; return 0; } what is value of x in c programming.

• 0
• 1
• True
• False
• 1

The CORRECT formula for the sentence, “not all rainy days are cold” is

• ∀d(Rainy (d)∧¬cold(d))
• ∃d(Rainy (d)∧¬cold(d))
• ∀d(¬Rainy (d)→cold(d))
• ∃d(¬Rainy (d)→cold(d))
• ∃d(Rainy (d)∧¬cold(d))

What is the first order predicate calculus statement equivalent to the following? "Everyone likes Someone." Where likes(x, y) represent x likes y.

• ∃y [∀x Likes (x, y)]
• ∀x [∃y Likes (x, y)]
• ∀x [∃y Likes (y, x)]
• ∃x [∃y Likes (x, y)]
• ∀x [∃y Likes (x, y)]

What is the first order predicate calculus statement equivalent to the following? " Someone is liked by Everyone ." Where likes(x, y) represent x likes y.

• ∃x [∀y Likes (y, x)]
• ∀x [∃y Likes (x, y)]
• ∀x [∃y Likes (y, x)]
• ∃x [∃y Likes (x, y)]
• ∃x [∀y Likes (y, x)]

Which one of the following is a graphical sequence?

• 1, 1, 1
• 4,2,2,1
• 3,3,3,3
• 3,3,2,2,1
• 3,3,3,3