If L1 and L2 are context free languages, which of the following is True about…

Let L1L_1L1​ and L2L_2L2​ be context-free languages (CFLs).

1️⃣ Is the intersection of two CFLs context-free?

No.
Context-free languages are not closed under intersection.

Example:
L1={aibicj∣i,j≥0}L_1 = \{ a^i b^i c^j \mid i,j \ge 0 \}L1​={aibicj∣i,j≥0}
L2={aibjcj∣i,j≥0}L_2 = \{ a^i b^j c^j \mid i,j \ge 0 \}L2​={aibjcj∣i,j≥0}

L1∩L2={anbncn∣n≥0}L_1 \cap L_2 = \{ a^n b^n c^n \mid n \ge 0 \}L1​∩L2​={anbncn∣n≥0},
which is not context-free.